Guaranteed cost control for a class of uncertain linear switched generalized systems

For an uncertain linear switched generalized system, we investigate the systems' stability by the Lyapunov stability theory and design the state feedback guaranteed cost controller under arbitrary switching laws. At the same time, we also give the upper bound of the performance index of the closed-loop system. Further we transform the guaranteed cost controllers' design problem into a set of linear matrix inequalities' solvability problem. Finally, we give an example to show our method is effective and feasible.