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.

Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions / Iervolino, Raffaele; Stephan, Trenn; Vasca, Francesco. - (2017), pp. 5894-5899. (Intervento presentato al convegno 56th IEEE Conference on Decision and Control tenutosi a Melbourne (Australia) nel 12-15 Dicembre 2017) [10.1109/CDC.2017.8264551].

Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions

Raffaele Iervolino
Writing – Original Draft Preparation
;
VASCA, FRANCESCO
2017

Abstract

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.
2017
978-1-5090-2873-3
Stability of piecewise affine systems through discontinuous piecewise quadratic Lyapunov functions / Iervolino, Raffaele; Stephan, Trenn; Vasca, Francesco. - (2017), pp. 5894-5899. (Intervento presentato al convegno 56th IEEE Conference on Decision and Control tenutosi a Melbourne (Australia) nel 12-15 Dicembre 2017) [10.1109/CDC.2017.8264551].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/709890
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