A novel hybrid observer that estimates the states of an oscillating system composed of a linear chain structure and an intrinsic pulse-modulated feedback is considered. This particular type of plant model appears in e.g. endocrine systems with pulsatile hormone secretion. The observer reconstructs the continuous states of the model as well as the firing times and weights of the feedback impulses. Since

In this paper we investigate stability of uniformly attracting sets for semiflows generated by impulsive infinite-dimensional dynamical systems without uniqueness. Obtained abstract results are applied to weakly nonlinear parabolic system, whose trajectories have jumps at moments of intersection with certain surface in the phase space.

Given an unstable hybrid stochastic functional differential equation, how to design a delay feedback controller to make it stable? Some results have been obtained for hybrid systems with finite delay. However, the state of many stochastic differential equations are related to the whole history of the system, so it is necessary to discuss the feedback control of stochastic functional differential equations

This paper investigates the exponential stability problem for a class of singularly perturbed impulsive systems in which the flow dynamics is unstable and is affected at discrete time instants by impulses that have both destabilizing and stabilizing effects. More precisely the impulses have stabilizing effects on the slow variables but destabilizing effects on the fast ones. Thus, a first contribution

We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete–continuous) linear switching systems on graphs, in which some modes correspond to discrete actions and some others correspond to continuous-time evolutions. Each discrete action has its own positive weight which accounts

This paper is concerned with the self-triggered filtering problem for a class of Markovian jumping nonlinear stochastic systems. The event-triggered mechanism (ETM) is employed between the sensor and the filter to reduce unnecessary measurement transmission. Governed by the ETM, the measurement is transmitted to the filter as long as a predefined condition is satisfied. The purpose of the addressed

In this paper, an efficient approach of modeling and control is presented for Multi-Rate Networked Control System (MRNCS) with considering long time delay. Firstly, the system is modeled as a switched system with a random switching signal which is subject to random networked-induced delay. For this, time delay is defined as a Markov chain and the model of MRNCS is obtained as a Markovian jump linear

Many real systems involve not only parameter changes but also sudden variations in environmental conditions, which often causes unpredictable topologies switching. This paper investigates the impulsive consensus problem of the one-sided Lipschitz nonlinear multi-agent systems (MASs) with Semi-Markov switching topologies. Different from the existing modeling methods of the Markov chain, the Semi-Markov

This paper studies the stochastic stability of positive Markov jump linear systems with a fixed dwell time. By constructing an auxiliary system that originated from the initial system with state jumps, sufficient and necessary conditions of stochastic stability for positive Markov jump linear systems are obtained with both exactly known and partially known transition rates. The main idea in the latter

This paper investigates the stabilization problem for a class of hybrid systems under state constraints. Emphasis is placed on the state constraints which are converted into the state saturation problem. Due to the existence of state saturation, the flow time consists of saturated and unsaturated time. Subsequently, sufficient conditions on uniformly globally pre-asymptotic stability (UGpAS) of hybrid

In this paper, the dissipative quantized control problem is addressed for Markov jump two-dimensional systems based on Roesser model, in which both asynchronous phenomenon and signal quantization between system modes and controller modes are taken into consideration simultaneously. Moreover, the hidden Markov model (HMM) is adopted to tackle such an asynchronous phenomenon. The principal goal is to

This paper is concerned with exponential quasi-dissipativity for switched nonlinear systems using multiple storage functions and multiple supply rates. First, a new concept of exponential quasi-dissipativity for a switched nonlinear system is proposed. In contrast with dissipative system which does not produce energy in some abstract sense, the supply rate of quasi-dissipativity is the sum of the conventional

This paper deals with the H∞ control problem for a class of switched non-linear systems with structural uncertainty using robust passivity, even though the control problem for none of subsystems is solvable. Firstly, when each subsystem is only required to be robust passive in the associated active region, the H∞ control problem for such a system is solved by designing a state-dependent switching law

The stability of Caputo fractional order switching systems is studied in the article by Wu C. etc (Wu and Liu (2019)). The authors claim that the lower bound of the Caputo fractional order derivative needs to be updated at each switching instant. However, the lower bound is relevant to the initial condition and reflects the historical information of a fractional system. No historical information can

This paper investigates the event-triggered sliding mode control (SMC) problem for singular systems with disturbance. Firstly, an event-triggered sliding mode control law is designed to guarantee the reachability of sliding surface. Different from the related methods, in order to deal with the difficulty caused by event-triggered SMC strategy, a novel Lemma is proposed in this paper. Secondly, the

This work focuses on optimal controls for hybrid systems of renewable resources in random environments. We propose a new formulation to treat the optimal exploitation with harvesting and renewing. The random environments are modeled by a Markov chain, which is hidden and can be observed only in a Gaussian white noise. We use the Wonham filter to estimate the state of the Markov chain from the observable

This paper is concerned with reliable robust sampled-data control for T–S fuzzy semi-Markov jump systems (SMJSs) with time-varying delay. The asynchronous model is established, which makes the fuzzy sampled-data controller share the premise variable of the fuzzy plant with the fuzzy system. By adjusting the free weight matrix in the concept of extended dissipative, H∞, L2−L∞, passive and Q,S,R-dissipative

This works is concerned with the finite-time optimal stabilization problem for a class of switched non-strict-feedback nonlinear systems whose powers are possibly different positive odd rational numbers in the sense the powers of each subsystem might differ from others. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping method

The problem of fixed-time stability of switched systems is studied. With the aid of the multiple Lyapunov function method, constraints on switching signals are derived under which global fixed-time stability of zero solutions of considered systems can be guaranteed. Sufficient conditions of fixed-time stability for Persidskii-type systems are obtained. The developed approaches are applied to the problem

This paper is concerned with the existence of a synchronized stationary distribution for stochastic multi-links systems with Markov jump (SMMJs). By employing Lyapunov method, Kirchhoff’s Matrix Tree Theorem in graph theory as well as M-matrix method, several criteria are given to guarantee the existence of a synchronized stationary distribution of SMMJs, including the Lyapunov-type theorem and a coefficients-type

In this paper, smooth output feedback controllers are presented to stabilize a class of planar switched nonlinear systems with asymmetric output constraints (AOCs). A new common barrier Lyapunov function (CBLF) is developed to prevent the switched system from violating AOCs. Combining the adding a power integrator technique (APIT) and the CBLF, state feedback controllers are designed. Then, reduced-order

In this paper, we propose an iterative approach for estimating the domains of attraction for a class of discrete-time switched systems, where the state space is divided into several disjoint regions and each region is described by polynomial inequalities. At first, we introduce the basic concepts of Multi-step state subsequence, Multi-step state subspace, Multi-step basin of attraction and Multi-step

The main purpose of this paper is to fill a gap in the literature concerning the problem of designing a sampled-data control law for continuous-time Lur’e systems. The goal is to design a state feedback sampled-data control for this class of nonlinear systems preserving global asymptotic stability and minimizing a guaranteed quadratic cost. The main challenge towards the solution of the proposed problem

The already proved Lum–Chua’s conjecture says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle. In this paper, we provide a new proof by using a novel characterization for Poincaré half-maps in planar linear systems. This proof is very short and straightforward, because this characterization avoids the inherent flaws

This paper studies scaled-based practical consensus issue for multiagent systems with input time delay by a fully continuous communication-free integral-type event-triggered scheme. By choosing the proper scales, scaled consensus can be induced to synchronization, bipartite consensus or cluster consensus. By defining a continuous communication-free measurement error for the integral-type event-triggered

We propose a compositional approach for constructing abstractions of general Markov decision processes (gMDPs) using approximate probabilistic relations. The abstraction framework is based on the notion of δ-lifted relations, using which one can quantify the distance in probability between the interconnected gMDPs and that of their abstractions. This new approximate relation unifies compositionality

Recent works have shown that the L1 and L∞-gains are natural performance criteria for linear positive systems as they can be exactly characterized by linear programs. Those performance measures have also been extended to linear positive impulsive and switched systems through the concept of hybrid L1×ℓ1-gain. For LTI positive systems, the L∞-gain is known to coincide with the L1-gain of the transposed

In this paper, we consider the non-autonomous semilinear impulsive differential equations with state-dependent delay. The approximate controllability results of the first-order systems are obtained in a separable reflexive Banach space, which has a uniformly convex dual. In order to establish sufficient conditions of the approximate controllability of such a system, we have used the theory of linear

In this paper, feedback control based on discrete-time state observations is used to study the inner synchronization of stochastic impulsive coupled systems (SICSs). Therein, the coupling strength of SICSs is state-dependent switching and time-varying under each switching. Besides, by means of average impulsive interval approach, the Lyapunov method and the graph theory, a synchronization criterion

In this paper, the mean-square exponential stabilization for stochastic differential equations with Markovian switching is studied. Specifically, a new set of sufficient conditions is derived to obtain the aperiodically intermittent control design which exponentially stabilizes the addressed hybrid stochastic differential equations. Further, stabilization problem by periodically intermittent control

The problem of fault identification in hybrid systems is investigated. It is assumed that the hybrid systems under consideration consist of a finite automaton, the set of nonlinear differential equations, and so-called mode activator that coordinates the action of these two parts. To solve the fault identification problem, sliding mode observers are used. The suggested approach for constructing sliding

Our purpose in this manuscript is to study the existence of solution, stability analysis and exact controllability results for an abstract integro hybrid evolution system with impulses on time scales. Non-linear functional analysis, evolution operator theory and Banach contraction theorem have been used to establish these results. In the end, we present some theoretical and numerical examples for different

This paper is concerned with the pth moment exponential stability of stochastic functional differential equations with impulses. Based on average dwell-time method, Razumikhin-type technique and vector Lyapunov function, some novel stability criteria are obtained for impulsive stochastic functional differential systems. Two examples are given to demonstrate the validity of the proposed results.

This paper investigates the problem of adaptive output feedback control for switched p-normal nonlinear systems with unknown homogeneous growth rate. A novel adaptive output feedback control scheme is first presented with the help of a dynamic gain technique, which renders the switched nonlinear systems with lower-triangular unknown homogeneous growth rate globally asymptotically stable. Then, the

A non-holonomic constant-speed robot travels in an unknown maze-like environment cluttered with complex obstacles. Through the obstacle-free part of the plane, the robot should autonomously arrive at the isoline where an unknown scalar field assumes a given value. Afterwards, it should track the obstacle-free part of the isoline. The robot has access only to the field value at the current location

This paper investigates the incremental stability and contraction via impulsive control for continuous-time dynamical systems (CDS). By using the methods of Lyapunov-like function and average dwell-time (ADT), criteria are established for incremental stability including incremental global asymptotic stability (δGAS) and incremental global exponential stability (δGES). The notion of rate of control

In this paper, the switched safe tracking control scheme is investigated for the attitude and altitude system of a medium-scale unmanned autonomous helicopter with output constraints and unknown external disturbances. To keep the attitude angles and altitude within the desired constrained range, an output boundary protection approach is adopted to generate an output constrained trajectory which is

This study addresses the stability and stabilizability problems for complex-valued memristive neural networks (CVMNNs) with actuator failures via reliable aperiodic event-triggered sampled-data control. Different from the traditional control methods with time-triggered mechanism, an aperiodic event-triggered sampled-data control scheme is first proposed for CVMNNs. Taking the influence of actuator

This paper investigates the dynamic event-triggered L∞ control for switched affine systems under limited communication resources. For switched affine systems, affine terms bring the difficulty on the exclusion of triggering Zeno behavior. The proposed dynamic event-triggered mechanism can preclude the occurrence of triggering Zeno behavior even if affine terms and the exogenous disturbance coexist

This paper addresses the issues of finite-time bounded (FTB) and finite-time H∞ control for nonlinear impulsive switched systems. By constructing appropriate multiple Lyapunov functions and employing mode-dependent average dwell time (MDADT) approach, some sufficient conditions are given to ensure that the system is FTB and finite-time H∞ controllable. Moreover, a hybrid dynamic output feedback controller

Temporal logics have lately proven to be a valuable tool for various control applications by providing a rich specification language. Existing temporal logic-based control strategies discretize the underlying dynamical system in space and/or time. We will not use such an abstraction and consider continuous-time systems under a fragment of signal temporal logic specifications by using the associated

In this paper, the stability problem is investigated for networked control systems. Input delays and multiple communication imperfections containing time-varying transmission intervals and transmission protocols are considered. A unified framework based on the hybrid systems with memory is proposed to model the whole networked control system. Hybrid systems with memory are used to model hybrid systems

The main objective of this paper is to study the stability and stabilization problems for a class of impulsive switched systems with inappropriate impulsive switching signals under asynchronous switching. Here, “inappropriate” means that the impulse jump moment may be inconsistent with the asynchronous switching moment or the system switching moment. And “asynchronous” implies that the switching of

This paper investigates the stability of nonlinear variable-time impulsive differential systems with delayed impulses. By using the comparison principle, the Lyapunov method and inequality techniques, some sufficient conditions for quasi-uniformly asymptotic stability and quasi-exponential stability of a given solution of variable-time impulsive differential systems with delayed impulses are established

The main objective of this work is to propose a novel paradigm for the design of two layers of control laws for DC-bus microgrids in islanded mode. An intensive attention will be paid to the inner control level for the regulation of DC–DC electronic power converters, where the use of Hybrid Dynamical System theory will be crucial to formulate and exploit switching control signals in view of reducing

This article discusses the problem of exponential stability for a class of hybrid neutral stochastic differential delay equations with highly nonlinear coefficients and different structures in different switching modes. In such systems, the coefficients will satisfy the local Lipschitz condition and suitable Khasminskii-types conditions. The set of switching states will be divided into two subsets

This paper investigates the sampled-data-based consensus problem of multi-agent systems (MASs) under asynchronous denial-of-service (DoS) attacks. In order to describe asynchronous DoS attacks, a new definition of complete DoS attack and novel double-layer switched systems are proposed. A complete DoS attack refers to a DoS attack that consists of several consecutive successful DoS attacks. While a

The present paper proposes a new robust fault tolerant control (RFTC) design for continuous-time switched systems. The main objective is to design in an integrated way the couple (controller, observer) that allows to stabilize switched systems even in the presence of actuator faults. A state/fault estimation observer is designed to simultaneously estimate system state and actuator faults. Based on

This paper studies the finite-time stability (FTS) for a class of hybrid dynamical systems with deviating argument. An improved hybrid control scheme including sampled-data control as well as impulsive control is presented. Based on the theory of differential equations with piecewise constant argument of generalized type (PCAG) and the method of average impulsive interval (AII), several Lyapunov-based

The present study focuses on designing the integral sliding-mode control (ISMC) for generalized Takagi–Sugeno (T–S) fuzzy singular stochastic systems by involving the Markovian jump type of system parameters. Distinct to the existing works, the present paper concerns about the derivation of sufficient conditions that ensure the global stability of considered T–S fuzzy stochastic singular Markovian

We present an investigation of stochastic evolution in which a family of evolution equations in L1 are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP’s) on the space of integrable functions. We derive equations for the first moment and correlations (of any order) of such processes. We also introduce the mean of the process

The aim of this paper is to study the stochastic SIS epidemic model with general incidence functional response under regime-switching. We derive a sufficient and almost necessary condition for the extinction and permanence of the epidemic system. Moreover, the rate of all convergences of the solution are also established. Our work generalizes and improves many existing results. Precisely, we obtain

By using a novel average dwell time approach, the stability problem for discrete-time switched systems with stable and unstable modes is investigated. First, the so-called weighted average dwell time is proposed and applied to reduce the conservativeness of stability results for the studied system whose all modes are stable. Then, combination the slow and fast weighted average dwell time, new stability

This paper proposes a stability criterion for linear systems with multi-rate sampled data by constructing novel Lyapunov functionals. The systems are represented as linear systems with input delay. The Lyapunov functionals consist of a quadratic function, an integral term related to the sampling intervals of each sensor and looped-functionals related to the sampling intervals of whole systems. In the

This work focuses on a class of regime-switching jump diffusion processes with a countably infinite state space for the discrete component. Such processes can be used to model complex hybrid systems in which both structural changes, small fluctuations as well as big spikes coexist and are intertwined. The paper provides weak sufficient conditions for Feller and strong Feller properties and irreducibility

In this paper, motivated by the need for distributed control of multi-agent networks consist of switched affine systems, a distributed leader following consensus controller is developed. Different from most existing methods with affine control multi-agent systems, switched affine multi-agent systems face additional difficulties in the analysis and control, meanwhile affine diffusive coupling consensus

In this paper, we study the event-triggered control problem for a kind of nonlinear time-varying system. Generally speaking we use the Lyapunov stability theory to solve an event-triggered tracking control problem of non-holonomic mobile robots. Firstly, we propose a continuous tracking control law using nonlinear state feedback. Under some proper assumptions, we use the linearization technique to

In this paper, we are concerned with stochastic stability of nonlinear positive systems with random switching signals. The random switching signals are triggered by a stochastic process which is independent of the state of the system. Our results provide sufficient conditions on global asymptotic stability in stochastic sense for nonlinear positive systems when individual subsystems are stable and

In the study, the issues of observer-based fault estimation (FE) as well as active fault-tolerant control (FTC) are considered based on a series of Takagi–Sugeno (T–S) fuzzy models against time-varying delay. Utilizing these obtained (k−1)th messages, a new k-step T–S fuzzy fast adaptive FE method is suggested to construct this observer. And a full-order controller is suggested to make the closed-loop

In this paper, the stabilization and H∞ control are considered for switched port-controlled Hamiltonian systems (SPCHSs) with unstabilizable modes via energy-based multiple Lyapunov functions (MLFs) methods and mode-dependent average dwell time (MDADT) strategies, where an improved MDADT-based tradeoff method is developed by a time subsequence technique to govern the running time of the asymptotic