Stability analysis of singular systems

This paper deals with a refined qualitative analysis of motions of a broad class of continuous time-varying nonlinear singular differential systems. These systems consist of a finite number of first-order differential equations that cannot be set into the normal form. Some novel qualitative concepts, convenient for the description of solutions of singular systems, are introduced and analyzed. These concepts involve some inherent properties of singular systems. General sufficient conditions for these concepts are derived in terms of the existence of a suitable Lyapunov function. Also, for the subclass of singular systems considered, the construction of a Lyapunov function candidate that can be effectively applied in the analysis is proposed. The results obtained generalize some known results in stability theory.

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