Explicit convergence relations for a class of discrete LTV systems and its application to performance analysis of deterministic learning

Abstract

A class of linear time-varying (LTV) systems commonly appears in classical adaptive control and identification, in which the accurate identification of parameters is highly related to their exponential stability. However, there is limited research on explicit convergence relations for discrete LTV systems. In this article, the explicit convergence relation of a class of discrete LTV systems is first established, in which strict Lyapunov functions are constructed by considering the convergence properties of the interconnected unforced subsystems. Next, based on the derived explicit convergence relation, a performance analysis of deterministic learning under the sampling-data framework is established. We show that the learning speed and learning accuracy increase with the persistent excitation (PE) level and decrease with the identifier gain. Moreover, an optimal learning gain exists related to the identifier gains. To illustrate the results, simulation studies are included.