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On the robustness of stability for uncertain large-scale systems subjected to multiple time delays

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Abstract

The robustness problem of stability for large-scale uncertain systems with a class of multiple time delays is addressed in this paper. By applying the complex Lyapunov stability theorem, the matrix measure techniques, and norm inequalities, a new approach for solving a general case of the above problem is proposed. Several robust stability conditions, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability and exponential stability of the uncertain large-scale time-delay systems. Moreover, these obtained results can also be applied to the stabilization design.

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Abbreviations

ℝ:

real number field

ℂ:

complex number field

x :

x=(x 1,x 2,...,x n )TεR n

x T :

transpose of vectorx

x* :

complex conjugate transpose of vectorx

Re(·):

real part of (·)

∥x∥:

norm of vectorx; ∥x∥=(x*x)1/2

A T :

transpose of matrixA

A* :

complex conjugate transpose of matrixA

¯λ(·):

maximal absolute value of eigenvalue of matrixA

Μ(A) :

matrix measure of matrixA; Μ(A)=¯λ((A + A*)/2)

∥ A ∥:

induced norm of matrix A; ∥A∥=[¯λ(A*A)]1/2

¦aij ¦:

absolute value of element aij

¦ A¦:

{¦aij¦} for matrix A={aij}

A >B :

aij > bij for alli andj where A={aij} andB={bij}

z :

complex number

¯z :

complex conjugate ofz

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Authors and Affiliations

  1. Control System Laboratory, Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan 70101 Republic of China

    Tzuu-Hseng S. Li, Chien-Hua Lee & Fan-Chu Kung

Authors
  1. Tzuu-Hseng S. Li
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  2. Chien-Hua Lee
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  3. Fan-Chu Kung
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Additional information

Supported by National Science Council, Taiwan, Republic of China, Grant NSC83-0404-E006-001.

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Li, TH.S., Lee, CH. & Kung, FC. On the robustness of stability for uncertain large-scale systems subjected to multiple time delays. Circuits Systems and Signal Process 14, 563–586 (1995). https://doi.org/10.1007/BF01213955

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  • DOI: https://doi.org/10.1007/BF01213955

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