Engineering Transactions, 44, 3-4, pp. 411-432, 1996

Robust Stability of Dynamical System

A. Ossowski
Institute of Fundamental Technological Research, Warszawa
Poland

A general concept of the robust stability of uncertain nonlinear dynamical systems is given. By using the method of optimal Lyapunov functions, the robust stability analysis is performed in the general case of a multidimensional system described by ordinary differential equations. The presented approach is applied to the problem of stability of affine systems with nonstationary structural disturbances. An illustrative example of a perturbed oscillator is given.

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References

M. ESLAMI and D.L. RUSSEL, On stability with large parameter variations, IEEE Trans. on Aut. Control, AC - 25, 6, pp. 1231-1234, Dec. 1980.

D.S. BERNSTEIN and W.M. HADDAD, Robust stability and performance analysis for linear dynamic systems, IEEE Trans. on Aut. Control, 34, 7, pp. 751-758, July 1989.

A. OSSOWSKI, On the exponential stability of non-stationary dynamical systems, Nonlinear Vibration Problems, 23, pp. 109-121, PWN, 1989.

K.M.A. ZOHDY and N.K. LOH, Necessary and sufficient conditions of quadratic stability of uncertain linear systems, IEEE Trans. on Aut. Control, 35, 5, pp. 601-604, May 1990.

Y.T. JUANG, Robust stability and robust pole assignment of linear systems with structured uncertainty, IEEE Trans. on Aut. Control, 36, 5, pp. 635-637, May 1991.

A. OLAS, Optimal quadratic Lyapunov functions for robust stability problem, Dynamics and Control, 2, pp. 265-279, 1992.

M. ESLAMI, Optimization of stability bounds, SIAM Review, 35, 4, pp. 625-630, Dec 1993.

D.Q. CAO and Z.Z. SHU, Robust stability bounds for multi-degree-of-freedom linear systems with structured perturbations, Dynamics and Stability of Systems, 9, 1, pp. 79- 87, 1994.

A. MUSZYŃSKA and B. RADZISZEWSKI, Exponential stability as a criterion of parametric modification in vibration control, Nonlinear Vibration Problems, 20, pp. 175-191, PWN, 1981.

Z.A. SMITH, Asymptotic stability of x" + a(t)x' + x = 0, Quart. J. Math., Oxford (2), 12, pp. 123-126, 1961.

A. OSSOWSKI, Nonlinear stabilization of linear systems, Arch. of Control Sciences, Vol. 3 (XXXIX), No. 1-2, pp. 69-84, 1994.

F. MARCHETTI and P. NEGRINI, Several functions in the problem of the stability of motion, Actes du Collogue, EQUA-DIFF 73, Bruxelles - Louvain, 3-8, Septembre 1973.

R. BELLMAN, Stability theory of differential equations, Me Graw Hill, 1953.

J. MUSZYŃSKI, On some problems concerning pseudolinear equations, Nonlinear Vibration Problems (Second Conference on Nonlinear Vibrations, Warsaw 1962), 5, pp. 305-319, 1963.




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