Asynchronous Control of 2-D Semi-Markov Jump Systems Under Actuator Saturation

Abstract

This brief investigates the asynchronous control issue of two-dimensional (2-D) semi-Markov jump systems in Roesser model. The switch of subsystems is governed by a novel mode generation approach, where the index of system mode is determined by the sum of variables of two directions. Such an approach can remove the problem of mode ambiguousness effectively. The actuator saturation and inaccessible system mode are simultaneously taken into account in the design of an asynchronous controller. The conditions are established to guarantee the almost surely exponential stability of the system. Additionally, estimation of the region of attraction is obtained by solving an optimization problem related to linear matrix inequalities. Finally, a numerical example is studied to demonstrate the availability of the designed asynchronous controller.