Sampled-data observer-based nonlinear control for coupled semilinear fractional-order partial differential equation systems with time-varying delays

Abstract

In this paper, we consider observer-based sampled-data in space output feedback stabilization of coupled time-delayed systems governed by semilinear time fractional-order partial differential equations (TFPDEs) with spatially varying parameters. For such systems, the output feedback controller is sampled-data in space and continuous in time. Here, we suppose that the sampled-in-space intervals are bounded. Under point measurements (PMs) or averaged measurements (AMs), the sampled-data observation problem is first considered. With the designed nonlinear observer, the sampled-data observer-based controller is then proposed to asymptotically stabilize the resulting closed-loop system in terms of the fractional Halanay inequality and the fractional Lyapunov method. Numerical examples are provided to valid the efficiency of the suggested synthesis.