Output regulation of piecewise linear systems

This paper proposes the output regulation method for piecewise linear systems with dynamic error-feedback based on piecewise quadratic Lyapunov functions technique. By constructing piecewise quadratic Lyapunov functions for the closed-loop augmented systems, the existence of the output regulation controller is cast as the feasibility of a set of bilinear matrix inequalities (BMIs). The optimal output regulation controller, which guarantees that the error vector tends to zero with the maximal decay rate, can be obtained by solving a non-convex optimization problem under the BMIs constraints.