Input-to-state practical stability criteria of non-autonomous infinite-dimensional systems

Abstract

We develop tools for the investigation of input-to-state practical stability (ISpS) and integral input-to-state practical stability (iISpS) of non-autonomous infinite-dimensional systems in Banach spaces. Sufficient conditions of ISpS and iISpS are given based on indefinite Lyapunov functions. The practical stability analysis is accomplished with the help of scalar practical stable functions. Then, a construction of ISpS Lyapunov function for a class of non-autonomous evolutions equations is provided in Hilbert spaces. We propose the ISpS Lyapunov methodology to make it suitable for the analysis of ISpS w.r.t. inputs from -spaces. Furthermore, we illustrate the theory with an example of a semi-linear reaction-diffusion equation.