Sufficient condition for stable control of discrete-time systems with statistical process model

A method for investigating the stability of discrete-time control systems with statistical uncertainties in model parameters is presented. These uncertainties are due to estimation errors arising in the identification of the process model. A mutually independent representation of these errors is applied. The process model and a controller algorithm are investigated in a state-space form. The closed-loop system is considered to be an autonomous one, with some mutually independent statistics affecting the system coefficients. Sufficient conditions for stability of these systems are derived. The example of a second-order non-minimal-phase system with state-space linear quadratic-problem controller and pole-placement controller is discussed.