ABSTRACT

This paper presents a dynamic output feedback controller with determined order for the stabilization of a class of fractional-order system with nonlinear uncertain parameters with fractional order $0<\mathit{\alpha }<2$. Using stability theories of fractional-order systems and linear matrix inequalities (LMIs), some sufficient conditions in the LMI form are deduced to guarantee the robustness and asymptotic stabilization of the system. Designing a dynamic robust controller, along with all its useful features, leads to more unknown parameters in comparison with a static controller and makes controller design procedure more difficult due to more complex constraints that must be solved. In this paper, using proper lemmas and theorems, LMI techniques, and suitable solvers and parsers the difficulty of designing such controllers has been overcome. Simulation results of three different numerical examples illustrate that the proposed sufficient theoretical results are applicable and effective for tackling robust stabilization problems.

摘要

本文提出了一种具有确定阶数的动态输出反馈控制器，用于稳定一类分数阶非线性不确定参数的分数阶系统的稳定性。 $0<\mathit{\alpha }<\mathrm{2个}$。利用分数阶系统的稳定性理论和线性矩阵不等式（LMI），推导了LMI形式的一些充分条件，以保证系统的鲁棒性和渐近稳定性。与静态控制器相比，设计动态鲁棒控制器及其所有有用功能会导致更多未知参数，并且由于必须解决更复杂的约束，因此使控制器设计过程变得更加困难。在本文中，使用适当的引理和定理，LMI技术以及适当的求解器和解析器，克服了设计此类控制器的困难。三个不同数值示例的仿真结果表明，所提出的足够的理论结果适用于解决鲁棒稳定问题。