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Synthesis of absolutely stabilising controllers

Synthesis of absolutely stabilising controllers

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The synthesis of fixed order controllers for nonlinear systems with sector bounded nonlinearities is considered. The authors constructed an inner and outer approximation of the set of absolutely stabilising linear controllers by casting the closed loop system as a Lure–Postnikov system. The inner approximation is based on the well-known sufficient conditions that require strict positive realness (SPR) of open loop transfer function (possibly with some multipliers) and a characterisation of SPR transfer functions that require a family of complex polynomials to be Hurwitz. The outer approximation is based on the condition that the open loop transfer function must have infinite gain margin, which translates to a family of real polynomials being Hurwitz. The authors illustrate the proposed methodology through the construction of an inner and outer approximation of absolutely stabilising controllers for a mechanical system.


    1. 1)
      • M. Aizerman , F. Gantmacher . (1964) Absolute stability of regulator systems.
    2. 2)
      • E.N. Laguerre . Th́eorie des équations nuḿeriques. J. de Mathématiques pures et appliqués , 99 - 146
    3. 3)
    4. 4)
      • M. Krstic , I. Kanellakopoulos , P.V. Kokotovic . (1995) Nonlinear and adaptive control design.
    5. 5)
      • M.T. Ho . H′∞ PID controller design for Lure systems and its application to a ball and wheel apparatus. Int. J. Control , 1 , 53 - 64
    6. 6)
      • D. Siljak . (1969) Nonlinear systems: parameter analysis and design.
    7. 7)
      • V.M. Popov . Absolute stability of nonlinear systems of automatic control. Autom. Remote Control , 857 - 875
    8. 8)
      • S. Lefschetz . (1965) Stability of nonlinear control systems.
    9. 9)
      • M. Krein , M.A. Naimark . The method of symmetric and Hermitian forms in the theory of the separation of the roots of algebraic equations. Linear Multilinear Algebra , 265 - 308
    10. 10)
      • G. Polya , G. Szego . (1998) Problems and theorems in analysis II – theory of functions, zeros, polynomials, determinants, number theory, geometry.
    11. 11)
      • S.P. Bhattacharyya , H. Chapellat , L.H. Keel . (1995) Robust control: the parametric approach.
    12. 12)
    13. 13)
      • Banjerdpongchai, D.: `Parametric robust controller synthesis using linear matrix inequalities', October 1997, PhD, Stanford University, Department of Electrical Engineering.
    14. 14)
      • M.G. Safanov . (1980) Stability and robustness of multivariable feedback systems.
    15. 15)
      • R.W. Brockett , J.L. Willems . Frequency domain stability criteria – Parts I and II. IEEE Trans. Autom. Control , 255 - 261
    16. 16)
      • H.K. Khalil . (1988) Nonlinear systems.
    17. 17)
      • K. Narendra , J. Taylor . (1973) Frequency domain criteria for absolute stability.
    18. 18)
      • Malik, W.A.: `A new computational approach to the synthesis of fixed order controllers', December 2007, PhD, Texas A&M University, Department of Mechanical Engineering, College StationTX.
    19. 19)
      • W. Hahn . (1967) Stability of motion.

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