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Stability and Invariance Analysis of Uncertain Discrete-Time Piecewise Affine Systems

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3 Author(s)
Rubagotti, M. ; Nazarbayev Univ., Astana, Kazakhstan ; Trimboli, S. ; Bemporad, A.

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.

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Automatic Control, IEEE Transactions on  (Volume:58 ,  Issue: 9 )