Weighted input-to-output practical stability of non-autonomous infinite-dimensional systems with disturbances

Abstract

In this paper, we introduce a new concept of weighted input-to-output practical stability (WIOpS) and weighted integral-input-to-output practically stable (WiIOpS) for non-autonomous infinite-dimensional systems with disturbances. By using the notion of practical stable scalar functions, sufficient conditions for WIOpS and WiIOpS are derived. As a result, the robust global asymptotic output practical stability criteria of non-autonomous infinite-dimensional systems with zero input is also established via an indefinite Lyapunov function. Thus, we study the UWISpS of non-autonomous nonlinear evolution equations. Moreover, we discuss UWISS and UWiISS for linear non-autonomous infinite-dimensional control systems. A feedback law is provided for a class of semi-linear evolution equations by which the closed-loop system is uniform input-to-state practical stable (UISpS) with respect to disturbances acting in the input. Two examples are given throughout the paper to illustrate the theoretical results.