@incollection{eprints574,
       booktitle = {Decision and Control Conference},
       publisher = {IEEE},
         journal = {Proc. 39th IEEE Conf. on Decision and Control},
          author = {Alberto Bemporad and Fabio Danilo Torrisi and Manfred Morari},
           title = {Performance analysis of piecewise linear systems and model predictive control systems},
            year = {2000},
          volume = {5},
         address = {Sydney, Australia December, 2000},
           pages = {4957--4962},
        abstract = {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},
             url = {http://eprints.imtlucca.it/574/},
        keywords = {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}
}