Stability analysis and controller synthesis for continuous-time linear stochastic systems

Abstract

In this paper, we derive results for the stochastic stability analysis and controller synthesis for continuous-time stochastic system. The important feature considered here is the multiplicative nature of the stochastic uncertainty in system dynamics. We generalize the existing small-gain type results for stability of discrete-time system with stochastic uncertainty in feedback loop to continuous-time dynamics. Further, LMI-based computable necessary and sufficient conditions are provided for the mean square stability of feedback system. The proposed stability analysis results are used for the synthesis of dynamic robust stabilizing feedback controller with stochastic uncertainty in the feedback loop between the plant and the controller. Fundamental limitation result for the mean square stabilization of system over stochastic channels is presented. Finally, we demonstrate the proposed framework on pendulum on a cart system.