离散广义分段仿射系统的静态输出反馈控制

Static output feedback control of discrete-time piecewise affine singular systems

摘要:

为了消除离散广义分段仿射系统的非正则性和非因果性对控制系统性能的不利影响,研究了一类具有参数不确定离散广义分段仿射系统的鲁棒静态输出反馈控制问题．基于分段Lyapunov函数、投影定理和几个基本引理,提出了两种方法来设计使具有参数不确定广义分段仿射系统鲁棒容许的静态输出反馈控制器．利用这两种方法得到的控制器不仅可以保证系统的稳定性,而且可以保证系统的正则性和因果性．通过求解一组包含参变量的LMIs,可以得到保证广义分段放射系统容许的反馈控制器增益．仿真结果证明了所提设计方法的有效性．

Abstract:

This paper investigates the robust admissibility analysis and static output feedback controller synthesis for a class of discrete-time piecewise affine singular systems. Based on the piecewise Lyapunov functions combined with Projection lemma and some basic lemmas,two novel approaches based on sufficient linear matrix inequality (LMI) conditions to the static output feedback controller synthesis are developed for the piecewise affine singular systems. It is shown that the controller gains can be obtained by solving a family of LMIs parameterized by scalar variables, which can not only ensure the stability of systems, but also guarantee the regularity and causality of systems. Finally, the applicability of the suggested methodologies is demonstrated via some simulation examples.