Dissipativity-based asynchronous control for discrete-time singular Markov jump systems with multiplicative noises

The singular systems, which could widely describe more general systems and present traits of physical features, are discussed in this study. Taking the fact that noises always exist in the state and output measurement of one singular system into consideration, which may cause some errors and decrease system performance, this article devotes itself to the dissipative control for discrete-time singular Markov jump systems (SMJSs) with multiplicative noises. To deal with the asynchronous phenomena between the system modes and the controller modes, a set of Markov chains are constructed. To make sure the closed-loop singular system is dissipative, a set of sufficient conditions are derived based on the linear matrix inequalities, and then the asynchronous controller is designed to ensure that SMJSs are stochastically admissible and strictly dissipative. Finally, a simulation example is carried out to verify the correctness of the derived theorem. The designed asynchronous controller improves the robustness of the controller and overcomes the asynchronous phenomenon. This control method can be applied in the fields of robot control system.