Stochastic stability of linear quadratic controller over intermittent actuator inputs

In this paper, we analyze Lyapunov stability of linear quadratic controller, when control inputs are communicated to actuators over a lossy network. We study properties of stochastic Lyapunov function, and establish necessary and sufficient network conditions for ensuring boundedness of the function in steady state. These conditions essentially establish existence of critical probability of successful transmission; followed by computation of upper and lower bound on critical probability. We further establish upper and lower bound on convergence of Lyapunov function in steady state. This result illustrates the performance trade-off between stability and quality of underlying communication network.