Robust stabilizing controller design for the uncertain discrete-time linear switching systems

This paper discussed the discrete-time linear switching systems whose discrete mode transitions are caused by discrete disturbance events and have continuous state reset functions, in the presence of parameter uncertainty, state and control input bounds, the problem of robust stabilizing controller design is researched, and a method of static state feedback stabilizing controller is proposed. The relation between robust stability and existence of a robust controlled invariant set is constructed, and a test condition which can achieve in finite number steps is given. Based on the robust stability condition and the notation of linear un-saturation region for control input, the proposed robust stabilizing controller can be obtained by solving of a finite number of inequalities. At last, a numerical example is given to show the validity of the method.