H-infinity State Feedback Control of Discrete-time Piecewise Affine Systems

Authors:	Xie Lihua, Nanyang Technological University, Singapore Xu Jun, Nanyang Technological University, Singapore
Topic:	2.5 Robust Control
Session:	Robust Controller Synthesis
Keywords:	Discrete-time systems; Piecewise linear systems; H-infinity control; State feedback.

Abstract

This paper addresses the H-infinity state feedback controlproblem for discrete-time piecewise affine systems. Our mainobjective is to derive design methods that take into account thepartition information of the system so as to alleviate the designconservativeness embedded in conventional approaches where localLyapunov functions are required to possess some globalcharacteristics. To overcome the difficulty arising fromnon-positive definiteness of Lyapunov matrices, a transformationis introduced which converts the state feedback control probleminto a bilinear matrix inequality (BMI) problem. We proposeiterative linear matrix inequality (LMI) approaches to solve theBMI problem. Numerical examples demonstrate the effectiveness ofthe proposed design.