Guaranteed cost control for a class of uncertain switched linear systems

For a class of continuous-time switched linear systems with norm-bounded time-varying uncertainty and a quadratic cost index, the problem of designing guaranteed cost state feedback controllers was investigated. Using multiple Lyapunov functions technique, the sufficient condition for existence of such controllers is derived. The parameterized representation of the guaranteed cost controllers is given and the corresponding switching strategy is constructed. If some parameters are selected in advance, the condition can be converted to solvability problem of a set of certain linear matrix inequalities (LMIs). Furthermore, the design problem of the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing efficient convex optimization techniques. Finally, an example is given to illustrate the effectiveness of the proposed results.