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Stability Analysis of Discrete-Time Piecewise-Linear Systems: A Generating Function Approach
Kai Liu,Jianghai Hu,Yu Yao,Baoqing Yang,Xin Huo 제어·로봇·시스템학회 2014 International Journal of Control, Automation, and Vol.12 No.5
This paper studies the exponential stability of a class of discrete-time piecewise-linear systems (DPLS). Some basic properties of the proposed DPLS are established, which enables the generating function approach to be used for the system stability analysis. By introducing the generating functions of DPLS and showing their properties, a sufficient and necessary condition for the exponential stability of DPLS is derived. Furthermore, the maximum exponential growth rate of system trajectories can be obtained exactly by computing the radii of convergence of the generating functions. The algorithm for computing the generating functions is developed and two examples are given to demonstrate the proposed approach.