Global stabilization of semilinear systems using switching controls

This paper considers feedback stabilization of distributed semilinear systems using switching controls. The semilinear processes, together with the switched controllers, constitute a type of switched nonlinear system. Three kinds of stabilizabilities, namely weak, strong and exponential stabilizabilities, are investigated one by one. Sets of sufficient conditions are obtained for each case. A necessary condition for strong stabilizability is given. The stabilizing control is characterized using a minimization problem. Applications to parabolic and hyperbolic like equations are considered.