Liapunov Criteria for Stability in Lp Norm of Special Neutral Systems

In this paper we present further results concerning the 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. The methodology provides results in terms of the Lp norm for the non differentiated variable and does not require the preliminary check of the difference system part input-to-state stability. The initial conditions are allowed to be unmatched and piece-wise continuous. The Liapunov conditions are given without involving, not even formally, the solution.