## Global robust stability of time-delay systems with discontinuous activation functions under polytopic parameter uncertainties.(English)Zbl 1181.93067

Summary: This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of $$M$$-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of Linear Matrix Inequalities (LMIs), based on Lyapunov function and the properties of the convex sets. One numerical example demonstrates the validity of the proposed criteria.

### MSC:

 93D09 Robust stability 34D20 Stability of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations 15A39 Linear inequalities of matrices 93C15 Control/observation systems governed by ordinary differential equations
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