Robust stability of perturbed systems with time delays,

Abstract Motivated by dynamical system considerations, a number of new results on robust stability of perturbed polynomials have been recently obtained. In the literature under consideration, the perturbations are known only within given bounds and enter affine linearly into the polynomial coefficients. In this paper, this formulation is expanded to include time delays. Under a properness assumption, a necessary and sufficient condition for robust stability is developed. An example is given to illustrate application of the main result.

[1]  M. Marden.  Geometry of Polynomials , 1970 .

[2]  Ezra Zeheb,et al.  On robust Hurwitz and Schur polynomials , 1986 .

[3]  Takeshi Hirai,et al.  3 A necessary and sufficient condition , 1970 .

[4]  A. C. Bartlett,et al.  A necessary and sufficient condition for Schur invariance and generalized stability of polytopes of polynomials , 1988 .

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

[6]  B. Ross Barmish,et al.  Polytopes of Polynomials with Zeros in a Prescribed Region , 1988, 1988 American Control Conference.

[7]  B. Anderson,et al.  On robust Hurwitz polynomials , 1987 .

[8]  Ezra Zeheb,et al.  Necessary and sufficient conditions for root clustering of a polytope of polynomials in a simply connected domain , 1989 .

[9]  B. Barmish.  A Generalization of Kharitonov's Four Polynomial Concept for Robust Stability Problems with Linearly Dependent Coefficient Perturbations , 1988 .

[10]  Antonio Vicino,et al.  Some results on robust stability of discrete-time systems , 1988 .

[11]  H. Kokame,et al.  An Extension of Kharitonov's Theorem and its Application , 1987, 1987 American Control Conference.

[12]  Brian D. O. Anderson,et al.  On the robustness of low-order Schur polynomials , 1988 .

[13]  M. Saridereli,et al.  The stability of polynomials under correlated coefficient perturbations , 1987, 26th IEEE Conference on Decision and Control.

[14]  A. Olbrot,et al.  Finite spectrum assignment problem for systems with delays , 1979 .

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

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

[17]  B. R. Barmish,et al.  Robust Schur stability of a polytope of polynomials , 1988 .