The purpose of this paper is to describe in terms of mathematical models and systems theory the dynamics of interbank financial contagion. Such a description gives rise to a model that can be studied with mathematical tools and will provide a new framework for the study of contagion dynamics complementary to research by simulation studied so far. It provides a better understanding of such financial

We introduce the concept of |$\epsilon $|-uncontrollability for random linear systems, i.e. linear systems in which the usual matrices have been replaced by random matrices. We also estimate the |$\varepsilon $|-uncontrollability in the case where the matrices come from the Gaussian orthogonal ensemble. Our proof utilizes tools from systems theory, probability theory and convex geometry.

We investigate the problem of almost zeros of polynomial matrices as used in system theory. It is related to the controllability and observability notion of systems as well as the determination of Macmillan degree and complexity of systems. We also present some new results on this important invariant in the light of randomness and we prove an uncertainty type relation appearing in such ensembles of

For non-linear positive switched systems (NPSSs) with time-varying delay, the |$H_{\infty }$| estimation problem is addressed in this paper. Firstly, in light of T-S fuzzy modeling method, the considered NPSS is equivalently transformed into a switched positive T-S fuzzy system. Then, a less conservative |$H_{\infty }$| performance co1ndition is provided for the error system via presenting a new piecewise

This article deals with the approximate controllability of semilinear retarded integrodifferential equations with non-instantaneous impulses governed by Poisson jumps in Hilbert space. The existence of a mild solution is established by using stochastic calculus and a suitable fixed point technique. The approximate controllability of the proposed non-linear stochastic differential system is obtained

The paper concerned with the controllability of nonlinear fractional noninstantaneous (NI) impulsive integrodifferential stochastic delay system (ISDS). Some sufficient conditions for the controllability of fractional NI impulsive ISDS have been derived by the new approach of measure of noncompactness in finite dimensional space. This NI impulsive ISDS is more reliable for the evolution process in

AbstractWe define a new operational matrix of fractional derivative in the Caputo type and apply a spectral method to solve a two-dimensional fractional optimal control problem (2D-FOCP). To acquire this aim, first we expand the state and control variables based on the fractional order of Bernstein functions. Then we reduce the constraints of 2D-FOCP to a system of algebraic equations through the operational

AbstractIn the context of maximizing cumulative dividends under barrier policies, generalized Azéma–Yor (draw-down) stopping times receive increasing attention during these past years. Based on Pontryagin’s maximality principle, we illustrate the necessity of such generalizations under the framework of spectrally negative Markov processes. Roughly speaking, starting from the explicit expression of

This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and geometries. For these systems, a partitioned finite element method (PFEM) is derived, based on the integration by parts of one of the two conservation laws written

AbstractThe feedback synthesis problem for a chain of integrators system with continuous bounded unknown perturbation is considered. Our approach is based on the controllability function (CF) method proposed by V.I. Korobov. The perturbation range is determined by the negativity condition for the total derivative of the CF with respect to the perturbed system. The control that does not depend on perturbation

Detecting the Pareto optimal points on the Pareto frontier is one of the most important topics in multiobjective optimal control problems (MOCPs). This paper presents a scalarization technique to construct an approximate Pareto frontier of MOCPs, using an improved normal boundary intersection (NBI) scalarization strategy. For this purpose, MOCP is first discretized and then using a grid of weights

AbstractThis paper considers the well posedness and the exponential stabilization problems of a cascaded ordinary differential equation (ODE)–partial differential equation (PDE) system. The considered system is governed by a linear ODE and the one-dimensional linear Korteweg–de Vries (KdV) equation posed on a bounded interval. For the whole system, a control input delay acts on the left boundary of

AbstractIn this paper, the stabilization of coupled regime-switching jump diffusion with Markov switching topologies (CRJDM) is discussed. Particularly, we remove the restrictions that each of the switching subnetwork topologies is strongly connected or contains a directed spanning tree. Furthermore, a feedback control based on discrete-time state observations is proposed to make the CRJDM asymptotically

AbstractThe port-Hamiltonian (pH) theory for distributed parameter systems has developed greatly in the past two decades. The theory has been successfully extended from finite-dimensional to infinite-dimensional systems through a lot of research efforts. This article collects the different research studies carried out for distributed pH systems. We classify over a hundred and fifty studies based on

AbstractWe discuss boundary control of a wave equation with a non-linear anti-damping boundary condition. We design structured finite-dimensional $H_{\infty }$-output feedback controllers that stabilize the infinite-dimensional system exponentially in closed loop. The method is applied to control torsional vibrations in drilling systems with the goal to avoid slip-stick.

AbstractThe free surface motion in moving containers is an important physical phenomenon for many engineering applications. One way to model the free surface motion is by employing shallow water equations (SWEs). The port-Hamiltonian systems formulation is a powerful tool that can be used for modeling complex systems in a modular way. In this work, we extend previous work on SWEs using the port-Hamiltonian

AbstractThe notion of implicit port-Lagrangian systems for nonholonomic mechanics was proposed in Yoshimura & Marsden (2006a, J. Geom. Phys., 57, 133–156; 2006b, J. Geom. Phys., 57, 209–250; 2006c, Proc. of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto) as a Lagrangian analogue of implicit port-Hamiltonian systems. Such port-systems have an interconnection structure

AbstractWe study different representations of a given rational transfer function that represents a passive (or positive real) discrete-time system. When the system is subject to perturbations, passivity or stability may be lost. To make the system robust, we use the freedom in the representation to characterize and construct optimally robust representations in the sense that the distance to non-passivity

AbstractThe explosive growth of network data traffic puts new demands on traffic scheduling. In this paper, the scheduling algorithm based on the software-defined network (SDN) architecture is studied. Firstly, the SDN architecture was introduced, then an SDN-based adaptive multi-path load balancing algorithm was proposed and finally the algorithm was simulated on the Mininet simulation platform to

AbstractIn this paper, we propose an linear matrix inequality (LMI)-based design method to observer-based control problem of linear descriptor systems with multiple time-varying delays. The delay function can be continuous and bounded but not necessarily differentiable. First, by introducing a new set of improved Lyapunov–Krasovskii functionals that avoid calculating the derivative of the delay function

AbstractThis paper deals with the ship course tracking control problem in a novel inverse optimal control approach. The inverse optimal stabilization problem and inverse optimal gain assignment problem are firstly extended to general systems affine in the control with unknown control gain. It is shown that a sufficient condition to solve the inverse optimal control problem is the existence of a stabilization

AbstractThis work focuses on the sliding mode control (SMC) for a family of linear systems with uncertainties and time-varying delays. First, an integral switching surface is constructed to verify the robust asymptotic stability of the considered system and the results are extended to analyse the mixed $\mathscr{H}_{\infty }\big /$Passivity performance index. Thereafter, a suitable SMC law is developed

AbstractThis paper addresses a finite-time regulation problem for time-varying nonlinear systems in p-normal form. This class of time-varying systems includes a well-known lower-triangular system and a chain of power integrator systems as special cases. No growth condition on time-varying uncertainties is imposed. The control law can guarantee that all closed-loop trajectories are bounded and well

AbstractThe purpose of this paper is to discuss, by the use of the Balakrishnan’s epsilon method, a class of optimal control problems governed by continuous linear time invariant singular systems which have only a finite dynamic mode. The linear differential algebraic equation is handled using the epsilon technique to obtain a sequence of the calculus of variations problems. A convergence theorem is

AbstractThis paper provides a mathematical characterization of the robust (strong) H-infinity norm of an uncertain linear time-invariant system with discrete delays in terms of the robust distance to instability of an associated characteristic matrix. The considered class of uncertainties consists of real-valued, structured, Frobenius norm-bounded matrix uncertainties that act on the coefficient matrices

AbstractIn this paper, the control problem of microgrids (MGs)operating in islanded mode is approached from a passivity-based control perspective. A control scheme is proposed that, relying only on local measurements for the power converters included in the network representation, achieves both voltage regulation and power balance in the network through the generation of grid-forming and grid-following

This work deals with the bias reduction of approximations to two known estimators of diffusion processes from discrete observations: the innovation and quasi-maximum likelihood estimators. The bias reduction is obtained by means of convergent approximations to the predictions for the first two moments of the innovation process associated to a continuous-discrete filter of minimum variance. For finite

In this paper, we consider output tracking for a one-dimensional wave equation, where the boundary disturbances are either collocated or non-collocated with control. The regulated output and the control are supposed to be non-collocated with control, which represents a difficult case for output tracking of PDEs. We apply the trajectory planning approach to design an observer, in terms of tracking error

This paper focuses on finite-time boundedness (FTB) of a class of switched non-linear neutral systems in the presence of multiple disturbances. Based on Lyapunov analysis, Finsler’s lemma and the average dwell-time concept, sufficient conditions are extracted to guarantee the FTB of the system. Using these sufficient conditions, finite-time |${H}_{\infty }$| controllers are designed via state feedback

AbstractThe model under consideration in this paper describes a vibrating structure of an interfacial slip and consists of three coupled hyperbolic equations in one-dimensional bounded interval under mixed homogeneous Dirichlet–Neumann boundary conditions. The first two equations are related to Timoshenko-type systems and the third one is subject to the dynamics of the slip. The main problem we discuss

AbstractFor the multisensor time-varying networked mixed uncertain systems with random one-step sensor delays and uncertain-variance multiplicative and linearly dependent additive white noises, a new augmented state method with fictitious noises is presented, by which the original system is transformed into a standard system without delays and with uncertain-variance fictitious white noises. According

AbstractIn this work, we investigate the controllability results of a fractional integro-differential equation with non-instantaneous impulses on time scales. Banach contraction theorem and the non-linear functional analysis have been used to establish these results. In support, a numerical example with simulation for different time scales is given to validate the obtained analytical outcomes.

AbstractIn our manuscript, we organize a group of sufficient conditions of approximate controllability for second order nonlocal neutral differential evolution inclusions. Next, we develop the result to analyze approximate controllability of impulsive systems. Lastly, a model is presented for illustration of theory.

AbstractThis study concentrates on the problem of $H_\infty $ output tracking bumpless transfer control for a category of switched linear systems (SLSs). The $H_\infty $ output tracking bumpless transfer control problem is to ensure the SLSs to satisfy the bumpless transfer performance and the $H_\infty $ output tracking properties by co-design of a switching rule and a series of controllers. Firstly

AbstractThis paper reports an analysis on proxy-based sliding mode control (PSMC), which is a controller proposed by Kikuuwe & Fujimoto (2006, Proceedings of the 2006 IEEE International Conference on Robotics and Automation, pp. 25–30) originally for position control of robot manipulators. The describing function method is employed to investigate the chattering behavior of PSMC combined with a simple

AbstractIn this work, we investigate the question of designing a positive observer for a class of infinite dimensional linear positive systems. We present a new observer design based on a classical Luenberger-like observer. The proposed observer is positive. That is, it ensures that the state estimates are nonnegative at any time. The existence of such positive observers is proven by a specific choice

This paper establishes a stochastic synchronization method for a Markovian jump complex dynamical network (MJCDN) with time-delay and uncertainties. The considered Markovian structure is piecewise-homogeneous with piecewise-constant time-varying transition rates (TRs). Two Markovian signals are utilized to construct the piecewise-homogeneous Markovian structure. A low-level Markovian signal with time-varying

AbstractIn this paper, we investigate the stabilization problem of a cascade of a fractional ordinary differential equation (FODE) and a fractional reaction–diffusion (FRD) equation where the interconnections are of Neumann type. We exploit the partial differential equation backstepping method for designing a controller, which guarantees the Mittag–Leffler stability of the FODE-FRD cascade. Moreover

AbstractThe paper deals with the problem of stabilizing the equilibrium states of a family of non-linear non-autonomous systems. It is assumed that the nominal system is a linear controlled system with periodic coefficients. For the nominal controlled system, a new method for constructing a Lyapunov function in the quadratic form with a variable matrix is proposed. This matrix is defined as an approximate

Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems

Efficient numerical procedures are developed for model-order reduction of a class of discrete-time nonlinear systems. Based on the solution of a set of linear-matrix inequalities, the Petrov–Galerkin projection concept is utilized to set up the structure of the reduced-order nonlinear model that preserves the input-to-state stability while ensuring an acceptable approximation error. The first numerical

This paper provides a theory analysis of cooperative optimal control problem for leader-follower descriptor multi-agent systems. Based on the linear quadratic regulator theory, the state feedback controller is designed to guarantee the consensus of multi-agent systems and minimize a local performance index, which is independent of the graph topology, the control gain matrix is obtained by solving a

This paper is concerned with the discrete event-triggered dynamic output-feedback |${H}_{\infty }$| control problem for the uncertain networked control system, where the time-varying sampling, network-induced delay and packet losses are taken into account simultaneously. The random packet losses are described via the Bernoulli distribution. And then, the closed-loop system is modelled as an augmented

In this paper, we consider boundary stabilization for a one-dimensional wave equation subject to periodic disturbance. By regarding the periodic signal as a boundary output of a free wave equation, we transform the controlled plant into a coupled wave system. We first design a state observer for the coupled system to estimate the disturbance and the system state simultaneously. An output feedback control

This paper is concerned with a kind of first-order singular differential system with impulses. Based on the Schaefer fixed-point theorem, some new verifiable algebraic criteria are given to ensure the controllability of bounded solutions for the considered system. The results obtained in this paper not only achieve the controllability of the singular differential system with impulses for the first

This paper addressed the problem of asymptotic regional stabilization of a class of two-dimensional mixed Roesser models. Based on the analysis of the polynomial solution of the parameter dependent linear matrix inequality (LMI), the sufficient condition for the existence of the regional stabilization controller is obtained in terms of LMI. Moreover, the robust controller is also given to stabilize

This paper deals with the input–output linearization of non-linear time-varying delay systems. We introduce an extension of the Lie derivative for time-varying delay systems and derive sufficient conditions for the existence of a causal and bounded non-linear feedback linearizing the input–output behaviour of the system. Sufficient conditions ensuring the internal stability after output stabilization

In this paper, the finite-time stabilization of stochastic coupled systems on networks (SCSNs) is studied. Different from previous research methods, the method used in this paper combines Lyapunov method with graph theory, and some novel sufficient conditions are obtained to ensure finite-time stability for SCSNs. Meanwhile, the convergence time is closely related to topological structure in networks

In this paper, we consider data-sampling controllability of multi-agent systems (MASs), where the interconnection topology is directed and weighted and the nodes have generic linear kinetic dynamics. First, the asynchronous data sampling protocols and synchronous data sampling protocols are proposed, respectively. Then the discussions focus on deriving the necessary and sufficient conditions for data-sampling

This manuscript prospects the controllability criteria of non-instantaneous impulsive Volterra type fractional differential systems. By enroling an appropriate Gramian matrix that is often defined by the Mittag-Leffler function and with the assistance of Laplace transform, the necessary and sufficiency conditions for the controllability of non-instantaneous impulsive Volterra-type fractional differential

In this paper, the problem of finite-time tracking for nth-order uncertain nonlinear systems with unmatched uncertainties is addressed. Using a terminal synergetic manifold, a controller is provided to force the tracking error to the origin in finite time in the presence of unmatched uncertainties. With this method, chattering problem is completely removed without defining a new function. Lyapunov

In this paper, we are concerned with boundary output feedback stabilization of a transport equation with non-local term. First, a boundary state feedback controller is designed by a backstepping approach. The closed-loop system is proved to be exponentially stable by the equivalence between original and target system. Then, we design an output feedback controller based on an infinite-dimensional observer

It is well known that given the continuous-time AutoRegressive representation |$A\left ( \rho \right ) \beta \left ( t\right ) =0,$| where |$\rho $| denotes the differential operator and |$A\left ( \rho \right ) $| a regular polynomial matrix, we can always construct the smooth behaviour of this system, by using the finite zero structure of |$A\left ( \rho \right ) $|⁠. The main theme of this work

This paper studies stochastic boundedness of trajectories of a non-vanishing stochastically perturbed stable linear time-invariant system. First, two definitions on stochastic boundedness are presented, then, the boundedness is analyzed via Lyapunov theory. A theorem is proposed, which shows that under a condition on the Lipchitz constant of the perturbation kernel, the trajectories remain stochastically

A dynamic backstepping control method is proposed for non-linear systems in the pure-feedback form, for which the traditional backstepping method suffers from solving the implicit non-linear algebraic equation. This method treats the implicit algebraic equation directly via a dynamic way, by augmenting the (virtual) controls as states during each recursive step. Compared with the traditional backstepping

In this paper, a multi-dimensional Taylor network (MTN) output feedback tracking control of nonlinear single-input single-output (SISO) systems in discrete-time form is studied. To date, neural networks are generally used to identify unknown nonlinear systems. However, the neuron of neural networks includes the exponential function, which contributes to the complexity of calculation, making the neural

This paper develops an asynchronous mode-dependent repetitive control strategy with periodic event-based dynamic output feedback for periodic trajectory tracking of continuous-time switched systems subject to time-varying switching delays between system modes and controllers and limited communication capacity in the feedback channel. By employing the input delay approach, the overall system is modelled

This paper investigates the second-order consensus of multi-agent systems with mixed delays and uncertain parameters. On one hand, an adaptive pinning aperiodically intermittent control protocol is designed to make multi-agent systems reach the second-order consensus. Moreover, the intermittent control protocol can be designed to be aperiodic, which means each agent can only obtain the relative states’

This paper addresses trajectory tracking problem in mobile robots considering additive uncertainties. The controller design method is based on linear algebra theory. Numerical estimation techniques are used to estimate the uncertainty value in each sample time. The controller is calibrated by stochastic way using the Monte Carlo Experiment. In addition, the proof of convergence to zero of the tracking

This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this