Distributed Control for a Class of Spatially Interconnected Discrete-Time Systems

Abstract: This paper considers the analysis and synthesis of a spatially distributed controller for discrete-time spatially interconnected parameter-varying system. The system under consideration has both discrete time and space dynamics. The concept of quadratic separators (Iwasaki and Shibata, 2001), (Chughtai and Werner, 2007) has been extended to compute a measure of worst-case performance for such systems by solving an LMI problem. The use of quadratic separator allows a systematic search for a parameter dependent Lyapunov function, thus resulting in less conservative controllers. The problem of synthesizing controllers leads to a nonlinear matrix inequality, and a hybrid evolutionary-LMI approach to solving this problem, based on LMI solvers and genetic algorithms, is proposed in this paper. A design example illustrates the efficiency of the proposed method.