Simultaneous Stabilization of Linear Time Varying Systems by Linear Time Varying Compensation

  • P. R. Bouthellier
  • B. K. Ghosh
Part of the Progress in Systems and Control Theory book series (PSCT, volume 1)


The problem of stabilization of a linear time-invariant plant by a linear time-invariant output feedback compensator has been one of the most important problems in system theory. However, since many of the systems considered in practice are time-varying, it is important to generalize results well known in time-invariant systems theory (see [4], [5], [6], [7]) to the time-varying case. It is for this reason we consider the following problem:

Problem 1.1: (Stabilizability Problem) Given a discrete-time multi-input multi-output linear time-varying dynamical system, does there exist a linear time-varying dynamic compensator which robustly stabilizes the system in the closed-loop?


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  1. [1]
    P.R. BOUTHELLIER, Ph.D. Dissertation, Washington University in St. Louis, in preparationGoogle Scholar
  2. [2]
    P.R. BOUTHELLIER and B.K. GHOSH, A Stability Theory of Linear Time-Varying System, Proceedings of the 25th Annual AUerton Conference on Communication, Control and Computing (1987), 1172–1180.Google Scholar
  3. [3]
    CA. DESOER, Slowly Varying Discrete System xi+1 = Aixi, Electronic Letters 6, No. 11 (1970), 339–340.CrossRefGoogle Scholar
  4. [4]
    B.K. GHOSH, An Approach To Simultaneous System Design, I. Semialgebraic Geometric Methods, SIAM J. Control and Optimization 24, No. 3 (1986), 480–496.CrossRefGoogle Scholar
  5. [5]
    B.K. GHOSH, An Approach To Simultneous System Design II. Nonswitching Gain and Dynamic Feedback Compensation by Algebraic Geometric Methods, SIAM J. Control and Optimization 26, No. 4 (1988), 919–963.zbMATHGoogle Scholar
  6. [6]
    B.K. GHOSH, Transcendental and Interpolation Methods in Simultaneous Stabilization and Simultaneous Partial Pole Placement Problems, SIAM J. Control and Optimization 24, No. 6 (1986), 1091–1109.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    B.K. GHOSH and C.I. BYRNES, Simultaneous Stabilization and Simultaneous Pole Placement by Non-switching Dynamic Compensation, IEEE Trans, on Automatic Control AC-28, No. 6 (1983), 735–741.MathSciNetCrossRefGoogle Scholar
  8. [8]
    E.W. KAMEN, The Poles and Zeros of a Linear Time-Varying System, Linear Algebra and Its Applications 98 (1988), 263–289.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    E.W. KAMEN, P.P. Khagonekar and K.R. Poolla, A Transfer Function Approach to Linear Time-Varying Discrete-Time Systems, SIAM J. Control and Optimization 23, No. 4 (1985), 550–565.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    P.P. Khagonekar and K.R. Poolla, A Polynomial Matrix-Fraction Representations for Linear Time-Varying Systems, Linear Algebra and Its Applications 80 (1986), 1–37.MathSciNetCrossRefGoogle Scholar
  11. [11]
    I.M. SINGER and J.A. THORPE, “Lecture Notes on Elementary Topology and Geometry”, Scott, Foresman, Glenview, IL, 1967.Google Scholar
  12. [12]
    A.S. STUBBERUD, “Analysis and Synthesis of Linear Time-Varying Systems”, University of California Press, 1964.Google Scholar

Copyright information

© Birkhäuser Boston 1989

Authors and Affiliations

  • P. R. Bouthellier
    • 1
  • B. K. Ghosh
    • 1
  1. 1.Department of Systems Science & MathematicsWashington UniversitySt. LouisUSA

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