Stabilization of switched nonlinear systems with input constraints using convex optimization

This paper considers the problems of stabilization and disturbance rejection for a class of switched polynomial systems with bounded input constraints. Based on multiple Lyapunov function(MLF) and state-dependent switching, sufficient conditions are given in terms of polynomial matrix inequalities(PMIs), under which the trajectories of the resulting switched system starting from a bounded set will remain inside it or a larger bounded set, meanwhile, the occurrence of sliding motion will not destroy the established property. With the proposed conditions, the disturbance rejection can be formulated as constrained optimization problem. Moreover, polynomial annihilators are introduced to reduce the conservatism. The proposed condition can be verified by the sum of squares(SOS) technique, and a numerical example is given to illustrate the proposed approach.