On the theory of stability of discontinuous dynamical systems
Keywords:discontinuous systems, matrix-valued Lyapunov functions, stability, La-Salle invariance principle.
The theory of differential equations with a discontinuous right-hand side finds application in problems of motion control, in the study of systems with variable structure, in the analysis of automatic control systems with sliding regime and others. The purpose of this article is to present some results of the study of stability obtained for the specified class of systems based on the method of Lyapunov’s matrix-valued functions. These results are formulated in terms of the sign-definiteness of special matrices, which are used to estimate the change in the Lyapunov function and its generalized derivative.
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