Deterministic and stochastic robustness measures for discrete systems

Deterministic and stochastic Lyapunov theorems are used to demonstrate the robustness of a stable linear, time-variant, discrete-time nominal system to both unknown deterministic and stochastic perturbations. Time-domain conditions are presented on the appropriate deterministic or random characteristics of perturbations to maintain the proper stability behavior of the overall system. It is concluded that the novel robustness conditions proposed can find application in the feedback design of control systems where the closed-loop system is known to be stable with a certain degree, e.g. as in the case of linear quadratic optimal control with α-degree of prescribed stability