Passivity-based boundary control for stochastic delay reaction–diffusion systems

Abstract

This paper considers the passivity-based boundary control for stochastic delay reaction–diffusion systems (SDRDSs) with boundary input–output. Delay-dependent sufficient conditions are obtained in the sense of expectation for SDRDSs by the use of Lyapunov functional method, for the input strict passivity and the output strict passivity, respectively. Then delay-dependent sufficient conditions are presented to ensure the uncertainty SDRDSs to achieve the robust passivity. Moreover, by utilising the techniques of Green formula and Poincare's inequality, the difficulty is handled caused by the boundary input and boundary controller. Besides, the troubles brought by the existence of the stochastic term and uncertain parameters are resolved by stochastic inequality techniques. Finally, numerical simulations are provided to show the validity of our theoretical results.