Reference : Global Asymptotic Stability of Oscillations with Sliding Modes
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Global Asymptotic Stability of Oscillations with Sliding Modes
Goncalves, Jorge mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Proceedings of the 15th IFAC World Congress
Volume 15
15th IFAC World Congress
Jully 21 - 26, 2002
[en] Relay ; Global Stability ; Quadratic Surface Lyapunov Functions ; Impact Maps
[en] This paper explores a new methodology based on quadratic surface Lyapunov functions to globally analyze oscillations with sliding modes in relay feedback systems (RFS). The method consists in efficiently construct quadratic Lyapunov functions on switching surfaces that can be used to show that impact maps, i.e., maps from one switch to the next, are contracting. This, in turn, shows that the system is globally stable. Several classes of piecewise linear systems (PLS) were previously successfully analyzed with this methodology. In this paper, we consider PLS whose trajectories switch between subsystems of different dimensions. We present and discuss distinct relaxations leading to sufficient conditions of different conservatism and computationally complexity. The results in this paper open the door to the analysis of other, more complex classes of PLS.

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