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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Recommended by Editorial Board member Nam H. Jo under the direction of Editor Hyungbo Shim.
This work was partially supported by National Natural Science Foundation of China under grants NSFC 61074160, 61021002 and 61104193.
Yu Yao received his B.S., M.S. and Ph.D. degrees in Automatic Control from Harbin Institute of Technology, China in 1983, 1986 and 1990, respectively. He is currently a professor in Control and Simulation Center, Harbin Institute of Technology, China. His research interests include nonlinear systems, robust control and flight control.
Kai Liu received his B.S. degree in Mathematics from Jilin University, China, in 2007. He is currently a Ph.D. student in Control and Simulation Center, Harbin Institute of Technology, China. His research interests include stability analysis, hybrid systems, piecewise-linear systems and robust control.
Dengfeng Sun received his B.S. degree in Precision Instruments and Mechanology from Tsinghua University in 2000, He received his M.S. degree from Ohio State University in 2002 and his Ph.D. degree from University of California at Berkeley, USA in 2008. He is currently an assistant professor in School of Aeronautics & Astronautics Engineering, Purdue University, USA. His research interests include modeling, optimization and control of large scale networked systems.
Venkataramanan Balakrishnan received his B.S. degree in EE from Indian Institute of Technology, India in 1985. He received his Ph.D. degree in EE from Stanford University, USA in 1992. He is currently a professor and head of ECE, Purdue University, USA. His research interests include robust control, convex optimization and robotics.
Jian Guo received his B.S. and M.S. degrees from Harbin Institute of Technology, China, in 2007 and 2009, respectively. Now he is a Ph.D. candidate in Harbin Institute of Technology. His research interests include spacecraft attitude dynamics and control; spacecraft guidance and navigation; saturation control theory.
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Yao, Y., Liu, K., Sun, D. et al. An integral function approach to the exponential stability of linear time-varying systems. Int. J. Control Autom. Syst. 10, 1096–1101 (2012). https://doi.org/10.1007/s12555-012-0603-2
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DOI: https://doi.org/10.1007/s12555-012-0603-2