Feedback Stabilization of Cyber-Physical Systems for Sampled-Data Control: Synthesizing the Cyber and the Physical With Closed-Loop Interactions

Inspired by the cyber-physical systems (CPS) of numerical methods for stochastic differential equations, we present a CPS model of sampled-data control systems (typically a synonym for computer control systems), which regards the intersection of the physical and the cyber (the key feature of CPS). As a theoretic foundation, we develop by the Lyapunov method a stability theory for a general class of stochastic impulsive differential equations (SiDE) which is formulated as a canonical form for CPS that may work in feedback loops and thus include those of sampled-data control systems. Applying the fundamental theory, we study stability of the CPS, which implies that of the sampled-data control system. By our CPS approach, we not only obtain stability criteria for the CPS of sampled-data control systems but also reveal the equivalence and intrinsic relationship between the two main approaches (viz. controller emulation and discrete-time approximation) in the literature. As the applications of our CPS theory, we propose a control design method for feedback stabilization of the CPS of sampled-data stochastic systems. Illustrative examples are conducted to verify that our method significantly improves the existing results. In this paper, we initiate the study of a systems science of design for CPS. This provokes many open and interesting problems.