Stabilisation of stochastic delay Markovian reaction-diffusion systems via boundary control

• Published in: IET control theory & applications 2019-10, Vol.13 (15), p.2436-2446
• Main Authors: Wu, Kai-Ning, Han, Xin-Xin, Zhang, Wei-Hai
• Format: Article
• Language: English
• Subjects: asymptotic stability; boundary control law; boundary controller; delay systems; delay‐dependent sufficient condition; Lyapunov methods; Lyapunov–Krasovskii functional; Markov processes; mean square asymptotic stability; parametric uncertainty; Poincaré inequality; reaction‐diffusion systems; Research Article; robust boundary stabilisation; robust control; SDMRDSs; stochastic delay Markovian reaction‐diffusion systems; stochastic Markovian reaction‐diffusion systems; stochastic systems; sufficient criterion; time‐varying delays; uncertain systems
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2019.0391

This study considers asymptotic stability in the mean square sense for stochastic delay Markovian reaction-diffusion systems (SDMRDSs) via boundary control. Firstly, the authors present a boundary controller for the system. By constructing of a Lyapunov–Krasovskii functional and utilising of Poincaré inequality, a sufficient criterion of mean square asymptotic stability for SDMRDSs is established. Next, boundary control for stochastic Markovian reaction-diffusion systems (SMRDSs) with time-varying delays is also investigated, and a delay-dependent sufficient condition for SMRDSs under the boundary control law is obtained. In addition, the robust boundary stabilisation of SMRDSs with parametric uncertainty is considered. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed results.