Stability and invariance analysis of uncertain discrete-time piecewise affine systems

Matteo Rubagotti, Sergio Trimboli, Alberto Bemporad

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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 {\cal X} of states. The approach relies on introducing fake dynamics outside {\cal 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 {\cal 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 {\cal 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 {\cal X}.

Original languageEnglish
Article number6475975
Pages (from-to)2359-2365
Number of pages7
JournalIEEE Transactions on Automatic Control
Volume58
Issue number9
DOIs
Publication statusPublished - 2013

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Invariance
Lyapunov functions
Asymptotic stability
Linear programming
Dynamical systems
Trajectories
Control systems

Keywords

  • Model predictive control (MPC)
  • piecewise affine (PWA)
  • piecewise quadratic (PWQ)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

Stability and invariance analysis of uncertain discrete-time piecewise affine systems. / Rubagotti, Matteo; Trimboli, Sergio; Bemporad, Alberto.

In: IEEE Transactions on Automatic Control, Vol. 58, No. 9, 6475975, 2013, p. 2359-2365.

Research output: Contribution to journalArticle

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