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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.

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This paper introduces a novel and rapid approach for the stability and performance analysis of linear time-varying (LTV) systems, which has a very wide application to the evaluation of control system of Aerospace vehicles. By introducing the concept of integral function for the LTV systems and showing its prosperities, a sufficient and necessary condition for the exponential stability of LTV systems is derived. Furthermore, by computing the radii of convergence of the integral function, the exponential decay rate of system trajectories of LTV systems can be obtained exactly, which provides a computable way for the analysis of system performance. Finally, the algorithm for computing the integral function is developed and the proposed approach is applied to the stability and performance analysis of the control system of international space station.