Remarks on the state convergence of nonlinear systems given any Lp input

In this paper, we study the state convergence of L^p-stable systems and input-to-state stable (ISS) systems given any L^p input signal where p isin [1, infin). Under some conditions on the system equations, it is shown that if the system is dissipative with a proper storage function H and supply rate s (y, u) = parupar^p - kparypar^P, k > 0 and it is zero-state detectable then the state x of the system converges to zero for any L^P input. This implies also that the system is also L ^p-stable. Using the same technique, if the system is ISS, under some conditions on the system equations and on the smooth ISS Lyapunov function, then the state x of the system converges to zero for any L^p input