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Exponential stability analysis of planar piecewise-linear systems: An integral function approach

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Abstract

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.

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Authors and Affiliations

  1. Harbin Institute of Technology, Harbin, China

    Kai Liu

  2. Purdue University, Purdue, USA

    Kai Liu

  3. the Control and Simulation Center, Harbin Institute of Technology, Harbin, China

    Yu Yao & Baoqing Yang

  4. the School of Electrical and Computer Engineering, Purdue University, Purdue, USA

    Venkataramanan Balakrishnan

  5. Harbin Institute of Technology, Harbin, China

    Yang Guo

Authors
  1. Kai Liu
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  2. Yu Yao
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  3. Baoqing Yang
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  4. Venkataramanan Balakrishnan
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  5. Yang Guo
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Corresponding author

Correspondence to Kai Liu.

Additional information

Recommended by Editorial Board member Izumi Masubuchi under the direction of Editor Hyungbo Shim.

This work was supported by National Natural Science Foundation of China under grants NSFC 61074160, 61021002, and 61104193.

Kai Liu received his B.S. degree in Mathematic from Jilin University, China in 2007. He is currently a joint Ph.D. student of Automatic Control in Harbin Institute of Technology, China and Purdue University, USA. His research interests include hybrid systems, piecewiselinear systems and robust control.

Yu Yao received his B.S., M.S. and Ph.D. degrees in Automatic Control, in 1983, 1986 and 1990, respectively, all from Harbin Institute of Technology, China. He is currently a professor in Control and Simulation Center, in Harbin Institute of Technology, China. His research interests include robust control, nonlinear systems and flight control.

Baoqing Yang received his B.S., M.S. and Ph.D. degrees in Automatic Control in 2003, 2005 and 2009, respectively, from Harbin Institute of Technology, China. He is currently a professor in Control and Simulation Center, in Harbin Institute of Technology, China. His research interests include predictive control and flight control.

Venkataramanan Balakrishnan received his B.S. degree in Electrical Engineering from Indian Institute of Technology, India in 1985, and his Ph.D. degree in Electrical Engineering from Stanford University, USA in 1992. He is currently a professor and head of School of Electrical and Computer Engineering, Purdue University, USA. His research interests include robust control, convex optimization and robotics.

Yang Guo received his B.S. and M.S. degrees in Xi’an Research Institute of High-Tech, China, in 2005 and 2008, respectively. Now he is a Ph.D. candidate in Harbin Institute of Technology. His research interests include Finite time Stabilization, Control.

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Liu, K., Yao, Y., Yang, B. et al. Exponential stability analysis of planar piecewise-linear systems: An integral function approach. Int. J. Control Autom. Syst. 10, 203–212 (2012). https://doi.org/10.1007/s12555-012-0201-3

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  • DOI: https://doi.org/10.1007/s12555-012-0201-3

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