Feedback stabilizability of cyber–physical systems for stochastic linear-quadratic control of sampled-data systems

Feedback stabilizability plays a pivotal role in stochastic linear-quadratic (SLQ) control problems in infinite horizon. A key question how to preserve the feedback stabilizability of the stochastic differential equation (where both the drift and diffusion contain control) in the sampled-data system naturally arises when the control law is discretized and implemented on a sampler and zero-order-hold device, which, however, has been seldom addressed. Sampled-data control systems are a typical class of cyber–physical systems (CPS). To address this key question, we establish a CPS theory for feedback stabilizability of sampled-data stochastic systems. Based on the feedback stabilizability, we further develop the CPS theory for stochastic $H_{\infty }$ control of sampled-data systems. Applying the CPS theory, we propose useful $H_{\infty }$ control design methods for sampled-data stochastic systems. Numerical examples are conducted to verify the effectiveness of our proposed methods. By our CPS theory, we initiate the study of SLQ problems for sampled-data systems, which evokes many interesting questions.