%0 Book Section
%A Bemporad, Alberto
%A Torrisi, Fabio Danilo
%A Morari, Manfred
%B Decision and Control Conference
%C Sydney, Australia December, 2000
%D 2000
%F eprints:574
%I IEEE
%K continuous piecewise affine function; feedback interconnection; feedback loops; hybrid systems; model predictive control systems; performance analysis; piecewise linear systems; plant model; prediction model; reachability analysis problem; stability domain; control system analysis; feedback; linear systems; predictive control; reachability analysis; stability
%P 4957-4962
%T Performance analysis of piecewise linear systems and model predictive control systems
%U http://eprints.imtlucca.it/574/
%V 5
%X Bemporad and Morari (1999) provided a tool for obtaining the explicit solution of constrained model predictive control (MPG) problems by showing that the control law is a continuous piecewise affine (PWA) function of the state vector. Therefore, the feedback interconnection between the MPC controller and a linear system, or a PWA system (e.g., a PWA approximation of a nonlinear system), is a PWA system. For discrete-time PWA and hybrid systems, the present authors (2000) presented an algorithm for verification/reachability analysis. In this paper, we formulate the performance analysis problem of closed-loop PWA systems (including MPC feedback loops where the prediction model and the plant model could be different) as a reachability analysis problem, and use our algorithm to obtain a tool for characterizing (i) the set of states for which the evolution is feasible, (ii) the domain of stability, (iii) the performance of the closed-loop