Robust Exponential Stability Analysis of Uncertain Discrete Time‐Varying Linear Systems

Abstract

This paper studies the robust exponential stability of uncertain discrete linear time-varying (UDLTV) systems. The key tool is the recently proposed generating functions. It can be found that a class of improved generating functions (IGFS) can fully characterize the robust exponential stability of UDLTV systems, and the maximum exponential decay rate of system trajectories can be computed by the radius of convergence of the IGFS. Moreover, the application of convex optimization technique and dynamic programming method provides an effective algorithm for the computation of the IGFS. Finally, the numerical example illustrates the efficacy and advantage of the proposed approach.