Mean Square Stability Analysis and Synthesis of Stochastic Continuous-time Linear Networked Systems

In this paper, we study the problem of stability analysis and controller synthesis of continuous-time linear networked systems in the presence of stochastic uncertainty. Stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output channels of the plant. We used the mean square notion for stochastic stability to address the analysis and controller synthesis problems of linear networked systems. These results generalize existing results on stability analysis and controller synthesis from discrete-time linear systems to continuous-time linear systems with multiplicative uncertainty. Necessary, sufficient conditions for mean square exponential stability are expressed in terms of the input-output property of deterministic or nominal system dynamics captured by the mean square system norm and variance of channel uncertainty. The stability results can also be interpreted as small gain theorem for continuous-time stochastic systems. Linear Matrix Inequalities (LMI)-based optimization formulation is provided for the computation of mean square system norm for stability analysis and controller synthesis. For a special case of single input channel uncertainty, we also prove a fundamental limitation result that arise in the mean square exponential stabilization of continuous-time linear systems. Simulation results are presented for WSCC 9 bus power system to demonstrate the application of developed framework.