Abstract
This paper addresses the H∞ state feedback control problem for discrete-time piecewise affine systems. Our main objective is to derive design methods that take into account the partition information of the system so as to alleviate the design conservativeness embedded in conventional approaches where local Lyapunov functions are required to possess some global characteristics. To overcome the difficulty arising from non-positive definiteness of Lyapunov matrices, a transformation is introduced which converts the state feedback control problem into a bilinear matrix inequality (BMI) problem. We propose iterative linear matrix inequality (LMI) approaches to solve the BMI problem. Numerical examples demonstrate the effectiveness of the proposed design.
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