基于观测器的离散广义分段仿射系统H_∞控制

Observer-based H_∞ control of discrete-time piecewise-affine singular systems with uncertain parameters

针对一类当前所处作用域未知的离散时间广义分段仿射系统,考虑其具有范数有界形式的时变参数不确定性,而且不能从测量输出获得的问题,研究此类系统基于观测器H_∞控制器的设计方法。闭环系统反馈控制器设计从离散广义分段仿射Lyapunov判据出发,应用相关基本引理将控制器存在条件转化为包含参变量的线性矩阵不等式形式,并采用投影定理进一步降低系统保守性,使得基于观测器的闭环系统满足一定的鲁棒H_∞性能指标。通过求解一组包含参变量的线性矩阵不等式组,得到保证此闭环系统具有鲁棒H_∞性能指标的反馈控制器增益和基于输出的观测器增益,并完成了基于Matlab 7.0线性矩阵不等式工具箱的数值仿真。仿真结果表明基于定理1所提控制器设计方法得到的闭环系统干扰抑制度γ=21.4254,且在系统矩阵取值不同的情况下,定理1较传统控制器设计方法具有更好的保守性。

For a class of discrete-time piecewise-affine singular systems with norm-bounded time varying parameters, a key issue is that the currently active region of the system is unknown, and it can＇t be inferred from the measured outputs. A novel observer-based control scheme for discrete-time piecewise-affine singular systems possessing H∞ performance is presented. By using the piecewise-affine singular Lyapunov functions and combined with Projection lemma and some basic lemmas, an approach for designing observer-based robust feedback controller is given with the H performance of the system being ensured. It is shown that the controller gains can be obtained by solving a family of Linear Matrix Inequality parameterized by scalar variables. The feedback controller gain and observer-based controller gain are obtained, which can ensure the stability of systems. The H∞ performance of the piecewise-affine singular systems is also guaranteed, and the numerical simulation based on Matlab 7.0 linear matrix inequality toolbox is completed. The simulation results show that the closed-loop system interference suppression index γ is 21.4254 based on the controller design method proposed by Theorem 1, which has better conservatism than the traditional controller design method in the case of with different system matrix values.