Controller design of switched linear systems

This paper is about controller design for switched linear systems with input signals. The synthesis problem of how to design the individual feedback gains and how to switch among the individual closed-loop feedback systems such that the switched system becomes (exponentially) stable, is constructively formulated as a bilinear matrix inequality problem. By using multiple quadratic Lyapunov functions, one for each closed-loop linear vector field, 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.