Quadratic stabilization of a switched affine system about a nonequilibrium point

This work deals with the problem of quadratic stabilization of switched affine systems, where the state of the switched system has to be driven to a point ("switched equilibrium") which is not in the set of subsystems equilibria. Quadratic stability of the switched equilibrium is assessed using a continuous Lyapunov function, having piecewise continuous derivative. A necessary and sufficient condition is given for the case of two subsystems and a sufficient condition is given in the general case. Two switching rules are presented: a state feedback, in which sliding modes may occur, and an hybrid feedback, in which sliding modes can be avoided. Two examples illustrate our results.