基于观测器的分段仿射离散系统H_∞控制

Observer-Based H_∞ Control of Discrete-Time Piecewise Affine Systems

针对分段仿射离散系统,提出一种基于观测器的H∞控制器设计方法。采用分段二次Lyapunov函数构造耗散不等式,以保证闭环系统的稳定性和H∞性能。通过椭球体近似逼近凸多面体形式的作用域,并借用奇异值分解技术处理矩阵等式约束,从而把H∞性能指标最小化问题转化为线性矩阵不等式(Linear matrix inequality,LMI)描述的凸优化问题,并运用LMI工具箱求解。最后通过仿真实例说明所提方法的可行性。

An observer-based H∞ controller design method for discrete-time piecewise affine systems is presented. The basic idea is to construct dissipation inequality with piecewise-quadratic Lyapunov func- tion to guarantee the stability and H∞ performance of the closed-loop systems. By approximating poly- topic operating regions with ellipsoids and using the singular value decomposition technique to treat the constraint of matrix equality, the minimum problem of the H∞ performance index is transformed as a convex optimization problem involving linear matrix inequalities （LMIs）, which are numerically feasible with commercially available LMI software. A numerical example is also given to verify the proposed the- oretical results.