Delay feedback control for switching diffusion systems based on discrete time observations

Li, Xiaoyue and Mao, Xuerong and Mukama, Denis S. and Yuan, Chenggui (2020) Delay feedback control for switching diffusion systems based on discrete time observations. SIAM Journal on Control and Optimization. ISSN 0363-0129 (In Press)

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    Abstract

    For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diusion systems. Response lags are required by most of physical systems and play a key role in the feedback control. The aim of this paper is to design delay feedback control functions based on the discrete-time observations of the system states and the Markovian states in order for the controlled switching diffusion system (SDS) to be exponentially stable in pth moment and probability one as well as stable in H1. The designed control principles are implementable to stablize quasi-linear and highly nonlinear SDSs. For quasi-linear SDSs the criteria are sharp that under the control with high strength the controlled SDSs will be stable (bounded) while under the weaker control they will be unstable (unbounded) in mean square. The sample and moment Lyapunov exponents are estimated which have close relationship with the time delays.