Necessary and sufficient conditions for robust oscillatory stability

The problem of robust oscillatory stability of uncertain systems is investigated in this article. For the uncertain systems, whose characteristic polynomial sets belong to the interval polynomial family or diamond polynomial family, sufficient and necessary conditions are given based on the stability and/or oscillation properties of some special extreme point polynomials. A systematic approach exploiting Yang's complete discrmination system is proposed to check the robust oscillatory stability of such uncertain systems. The proposed method is efficient in computation and can be easily implemented.

[1]  Roberto Tempo,et al.  A dual result to Kharitonov's theorem , 1990 .

[2]  V. Kharitonov.  Asympotic stability of an equilibrium position of a family of systems of linear differntial equations , 1978 .

[3]  Kenjiro Yoshimura,et al.  Dynamic stability analysis of an industrial power system , 1993 .

[4]  R. Billinton,et al.  Oscillatory stability considerations in transmission expansion planning , 1989 .

[5]  ASYMPTOTIC STABILITY OF AN EQUILIBRIUM P . OSITION OF A FAMILY OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS , 2022 .

[6]  N. Mithulananthan,et al.  Linear performance indices to predict oscillatory stability problems in power systems , 2004, IEEE Transactions on Power Systems.

[7]  Pei-Hwa Huang,et al.  Oscillatory Stability Considerations in Transmission Expansion Planning , 1989, IEEE Power Engineering Review.

[8]  B. Ross Barmish,et al.  New Tools for Robustness of Linear Systems , 1993 .

[9]  Shankar P. Bhattacharyya,et al.  Robust Control: The Parametric Approach , 1995 .

[10]  G. Ladas,et al.  Oscillation Theory of Delay Differential Equations: With Applications , 1992 .

[11]  D. S. Zinger,et al.  Characterization and snubbing of a bidirectional MCT switch in a resonant AC link converter , 1992 .

[12]  Huang Lin,et al.  Root locations of an entire polytope of polynomials: It suffices to check the edges , 1987, 1987 American Control Conference.

[13]  Lu Yang,et al.  A complete discrimination system for polynomials , 1996 .

[14]  Roberto Tempo,et al.  An extreme point result of robust stability of a diamond of polynomials , 1992 .

[15]  V. Lakshmikantham,et al.  Oscillation Theory of Differential Equations With Deviating Arguments , 1987 .

[16]  Dao Yi Xu.  Necessary and sufficient conditions for robust oscillation , 1996, Int. J. Syst. Sci..