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Exponential Stability Analysis of Planar Piecewise-Linear Systems: An Integral Function Approach
Kai Liu,Yu Yao,Baoqing Yang,Venkataramanan Balakrishnan,Yang Guo 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.2
This paper studies the exponential stability of continuous-time planar piecewise-linear systems (PPLS). By introducing a novel conception of integral function of PPLS and showing its properties, a sufficient and necessary condition for the exponential stability is derived. Furthermore, the exponential growth rate of system trajectories can be obtained accurately by computing the convergence radius of integral function. The algorithm for computing the integral function is developed and two examples are given to demonstrate the proposed approach.
An Integral Function Approach to the Exponential Stability of Linear Time-Varying Systems
Yu Yao,Kai Liu,Jian Guo,Dengfeng Sun,Venkataramanan Balakrishnan 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.6
This paper studies the exponential stability of linear time-varying (LTV) systems using the recent pro-posed integral function. By showing the properties of the integral function and applying the Bellman-Gronwall Lemma, a sufficient and necessary condition for the exponential stability of LTV systems is derived. Furthermore, the exponential decay rate of the system trajectories can be obtained by computing the radii of convergence of integral function. The algorithm for computing the integral function is also developed and two classical examples are given to illustrate the proposed approach.