%0 Journal Article
%@ 0018-9286
%A Rubagotti, Matteo
%A Trimboli, Sergio
%A Bemporad, Alberto
%D 2013
%F eprints:1811
%I IEEE 
%J IEEE Transactions on Automatic Control 
%K Model predictive control (MPC); piecewise affine (PWA);   piecewise quadratic (PWQ)  
%N 9
%P 2359-2365
%T Stability and Invariance Analysis of Uncertain Discrete-Time Piecewise Affine Systems
%U http://eprints.imtlucca.it/1811/
%V 58
%X This note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non-invariant set X of states. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function via linear programming. The existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset X of the state space, and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain X.