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Lyapunov criteria for stability in $$L_{p}$$ norm of special neutral systems. (English) Zbl 1244.93124
Summary: We present a Lyapunov–Krasovskii methodology for checking the global asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations coupled with continuous time difference equations, often referred to as special neutral systems, with unmatched and piecewise continuous initial conditions. The methodology provides results in terms of the $$L_{p}$$ norm for the non differentiated variable and does not require the preliminary check of input-to-state stability for the difference part of the system. Lyapunov conditions are given without involving, not even formally, the solution.

##### MSC:
 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93D25 Input-output approaches in control theory 93C15 Control/observation systems governed by ordinary differential equations 93C10 Nonlinear systems in control theory
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