An integral function approach to the exponential stability of linear time-varying systems |
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Authors: | Yu Yao Kai Liu Dengfeng Sun Venkataramanan Balakrishnan Jian Guo |
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Affiliation: | 1. Control and Simulation Center, Harbin Institute of Technology, Harbin, China 2. School of Aeronautics & Astronautics Engineering, Purdue University, Purdue, USA 3. School of Electrical and Computer Engineering, Purdue University, Purdue, USA
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Abstract: | This paper studies the exponential stability of linear time-varying (LTV) systems using the recent proposed 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. |
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