Robust non-fragile boundary control for non-linear parabolic PDE systems with semi-Markov switching and input quantization

Abstract

In this paper, the robust boundary control problem for non-linear PDE systems is discussed. Specifically, the PDE under investigation is of parabolic type with semi-Markov jumping signals subject to non-linearities and parameter uncertainties. The main goal of this paper is to devise a non-fragile boundary control law which assures the robust stabilization of the addressed system in spite of gain fluctuations and quantization in its design. In particular, to reduce the burden in the communication medium, the input signals can be quantized before transmitted to the actuator by using logarithmic quantizers. Moreover, by utilizing the Lyapunov stability theory and vector-valued Wirtinger’s inequality, a set of sufficient conditions for robust stabilization of the underlying system is established in the form of linear matrix inequalities (LMIs). Based on the obtained conditions, the existence of the desired controller is confirmed and an explicit form of the controller gains are developed. Eventually, the efficacious of the extracted theoretical results are manifested by virtue of two simulation examples.