Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions

Raffaele Iervolino, Stephan Trenn, Francesco Vasca

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State-dependent switched systems characterized by piecewise affine (PWA) dynamics in a polyhedral partition of the state space are considered. Sufficient conditions on the vectors fields such that the solution crosses the common boundaries of the polyhedra are expressed in terms of quadratic inequalities constrained to the polyhedra intersections. A piece-wise quadratic (PWQ) function, not necessarily continuous, is proposed as a candidate Lyapunov function (LF). The sign conditions and the negative jumps at the boundaries are expressed in terms of linear matrix inequalities (LMIs) via cone-copositivity. A sufficient condition for the asymptotic stability of the PWA system is then obtained by finding a PWQ-LF through the solution of a set LMIs. Numerical results with a conewise linear system and an opinion dynamics model show the effectiveness of the proposed approach.
Original languageEnglish
Title of host publicationProceedings of the 56th IEEE Conf. Decision Control (CDC 2017)
Number of pages6
Publication statusPublished - 2017
Externally publishedYes

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