Convergent piecewise affine systems: analysis and design Part I: continuous case

In this paper convergence properties for piecewise affine (PWA) systems are studied. The notions of exponential, uniform and input-to-state convergence are introduced and studied. For PWA systems with continuous right-hand sides it is shown that the existence of a common quadratic Lyapunov function for the linear parts of the system dynamics in every mode is sufficient for the exponential and input-to-state convergence of the system. For a class of PWA control systems we design (output) feedback controllers that make the closed-loop system input-to-state convergent. The conditions for such controller design are formulated in terms of LMIs. The obtained results can be used for designing observers and (output-feedback) tracking controllers for PWA systems.