Finite-region stabilization and H∞ control for 2-D FMLSS asynchronously switched system

Abstract In this paper, dwell time method incorporated with multiple Lyapunov-like functions are utilized to investigate the finite-region asynchronously switched control problems for 2-D switched system in the Fornasini-Marchesini local state-space (FMLSS) model. The finite-region stability (FRS) conditions for 2-D asynchronously switched FMLSS model are attained when there is no external disturbances. Then, the sufficient conditions in terms of dwell time scheme for the finite-region H∞ control of 2-D asynchronously switched FMLSS model are derived. Based on the established conditions, the sufficient solvability conditions for designing the corresponding finite-region mode-dependent state feedback controllers are given according to linear matrix inequalities (LMIs). Two numerical examples are employed to show the effectiveness of the provided design methods.