Synthesis of switched linear systems

This paper treats the following synthesis problem: given a switched linear system, how should the linear vector fields be selected among the possible ones such that the switched system becomes (exponentially) stable? In this paper, this synthesis problem is constructively formulated as a bilinear matrix inequality problem. The starting point for the design is existing stability conditions for switched and hybrid systems using multiple quadratic Lyapunov functions, one for each linear vector field. Using such a general piecewise quadratic Lyapunov function structure, a stabilizing controller is synthesized for a broader class of switched systems than earlier proposed in the literature. One example is given to illustrate the synthesis procedure.