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The Pushpa Publishing House proposes to organize a five day "International Conference on Mathematics of Date" from December 31, 2010 to January 04, 2011 scheduled to be held at Allahabad, India.

 
  Advances in Differential Equations and Control Processes  
 ISSN: 0974-3243
 
 
 

     Advances in Differential Equations and Control Processes
    Volume 3, Issue 1, Pages 19 - 31 (February 2009)


THE COMPUTATION OF A COMMON STANDARD QUADRATIC LYAPUNOV FUNCTION FOR TRIDIAGONAL SYSTEM

Miao Yu (P. R. China) and Yan Gao (P. R. China)

Received January 5, 2009

References:



[1] Z. Chen and Y. Gao, The computation of a common quadratic Lyapunov function for linear control system, J. Inform. Comput. Sci. 2 (2007), 299-304.

[2] D. Cheng, L. Guo and J. Huang, On quadratic Lyapunov functions, IEEE Trans. Automat. Control 48(5) (2003), 885-890.

[3] L. Gurvits and A. Samorodnitsky, A note on common quadratic Lyapunov functions for linear inclusions: exact results and open problems, Proc. IEEE Conf. Decision and Control, 2005, pp. 2350-2355.

[4] C. King and R. Shorten, A singularity test for the existence of common quadratic Lyapunov functions for pairs of stable LTI systems, Proc. Amer. Control Conf., 2004, pp. 3881-3884.

[5] B. Liu and Z. K. Zhang, Stability of nonlinear systems with tridiagonal structure and its applications, Acta Automat. Sinica 33(4) (2007), 442-445.

[6] R. N. Shorten and K. S. Narendra, Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a finite number of stable second order linear time-invariant systems, Int. J. Adaptive Control Signal Process. 16(10) (2002), 709-728.

[7] R. N. Shorten and K. S. Narendra, On common quadratic Lyapunov functions for pairs of stable LTI systems whose system matrices are in companion form, IEEE Trans. Automat. Control 48(4) (2003), 618-621.

[8] R. N. Shorten, K. S. Narendra and O. Mason, A result on common quadratic Lyapunov functions, IEEE Trans. Automat. Control 48(1) (2003), 110-113.

Keywords and phrases: switched systems, tridiagonal matrices, common standard quadratic Lyapunov functions.

 


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