Lyapunov criteria for stability in LpLp norm of special neutral systems

In this paper, 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 un-matched and piece-wise continuous initial conditions. The methodology provides results in terms of the LpLp 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. The Lyapunov conditions are given without involving, not even formally, the solution.