带极点约束离散广义分段仿射系统的H_∞保性能控制

Guaranteed cost control of discrete-time generalized piecewise-affine singular systems with pole placement

针对一类具有范数有界时变参数不确定性的离散时间广义分段仿射系统和一个二次型性能指标,研究具有极点约束的H∞最优保性能输出反馈控制律的设计问题。通过采用广义分段仿射Lyapunov函数、投影定理以及几个基本引理,提出了对于二次型性能指标使参数不确定离散广义分段仿射系统具有二次D-稳定性,且满足鲁棒H∞性能指标的静态输出反馈控制器的设计方法。通过求解一组包含参变量的LMIs,可以得到保证广义分段仿射系统既容许又满足二次型性能指标的H∞输出反馈控制器增益,仿真结果证明了所提设计方法的有效性。

For a class of discrete-time generalized piecewise-affine singular systems with norm-bounded time varying parameters uncertainties and a quadratic cost index, the problem of designing an optimal guaranteed cost H∞ output feedback controller with pole placement is considered in this paper. By using the generalized piecewise-affine singular Lyapunov functions combined with Projection lemma and some basic lemmas, an approach of designing a robust H∞ static output feedback controller is provided. This approach ensures the quadratic Dstability of the generalized piece-affine singular system with quadratic performance index. Specifically, it makes the parameter uncertain and it also satisfies the performance index of robust H∞. It is shown that the H∞ output feedback controller gains can be obtained by solving a family of LMIs parameterized by scalar variables, which both allows and satisfies the quadratic performance index. Finally, the applicability of the proposed method is demonstrated through some simulation exampies.