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

Rubagotti, Matteo and Trimboli, Sergio and Bemporad, Alberto Stability and Invariance Analysis of Uncertain Discrete-Time Piecewise Affine Systems. IEEE Transactions on Automatic Control , 58 (9). pp. 2359-2365. ISSN 0018-9286 (2013)

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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.

Item Type: Article
Identification Number: 10.1109/TAC.2013.2251774
Uncontrolled Keywords: Model predictive control (MPC); piecewise affine (PWA); piecewise quadratic (PWQ)
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 30 Sep 2013 12:23
Last Modified: 30 Sep 2013 12:23
URI: http://eprints.imtlucca.it/id/eprint/1811

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