Dissipativity based repetitive control for switched stochastic dynamical systems

This paper addresses the issues of dissipativity analysis and repetitive control synthesis for a class of switched stochastic dynamical systems with time-varying delay. By using the lifting technique, the considered one dimensional model is converted into a continuous-discrete stochastic two dimensional delayed model to describe the control and learning actions of the repetitive controller. By employing stochastic system theory together with Lyapunov function technique, a new set of sufficient conditions in terms of linear matrix inequalities (LMIs) is established such that the switched stochastic system in two dimensional delayed model is mean square asymptotically stable and (Q,S,R)(Q,S,R)-dissipative. Then, the desired repetitive controller is designed by solving a convex optimization problem established in terms of LMIs. More precisely, repetitive controllers with H∞, passivity and mixed H∞ and passivity performances can be obtained as the special cases for the considered system. Finally, numerical examples are provided to demonstrate the effectiveness and potential of the developed design technique.