Guaranteed cost control of uncertain discrete-time delay switched systems

For a class of discrete-time delay switched systems with norm bounded parameter uncertainty and a quadratic cost index, the problem of designing a suboptimal guaranteed cost state feedback controller is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by using a piecewise Lyapunov function approach together with linear matrix inequality technique, and the parameterized representation of the controllers is given in terms of linear matrix inequalities. Based on that, the design problem of the suboptimal guaranteed cost controller is turned into a convex optimization problem with linear matrix inequalities constraints. A numerical example demonstrates the effect of the proposed design approach.