Stability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functions

Matteo Rubagotti, Sergio Trimboli, Daniele Bernardini, Alberto Bemporad

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)


For piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set χ, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside χ and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing χ by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in χ. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set χ of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.

Original languageEnglish
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
Publication statusPublished - Jan 1 2011
Externally publishedYes

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670

ASJC Scopus subject areas

  • Control and Systems Engineering

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