A new switching strategy design for uncertain switched linear systems based on min-projection strategy in guaranteed cost control problem

An effective way to deal with uncertainties in control of uncertain switched linear systems is so-called guaranteed cost control (GCC). Existing works on the GCC of these systems only provide asymptotical stability analysis. This paper focuses on the GCC to provide exponential stability in these systems. To this end, we design a new switching strategy and a state-feedback controller to exponentially stabilize the GCC of continuous-time switched linear systems with norm-bounded uncertainties. First, a new switching strategy is designed based on the common Lyapunov function technique and min-projection strategy. Second, a sufficient condition on the existence of proposed switching strategy is presented in the form of linear matrix inequalities. It is proved that the system to be exponentially stable under applying this switching strategy and guaranteed cost value and convergence rate of states are calculated. Finally, some numerical examples and comparisons are performed.