Asymptotic stability for a class of linear discrete systems with bounded uncertainties

Abstract

2.47801m,,s -1.4471; 0.0518 I m22I -0.0194; 2 . 0 0 0 1 m~~~3 . 4 3 7 0 ; mq2= -0.7115; -0.0026s m 3 3 I -0.0012.We first show that this hyper-rectangle is strictly Hurwitz, i.e., that every matrix M E W is strictly Hurwitz. Since M is block diagonal, we can write where polynomials and matrices arising in robustness problems," in Proc. Conf. Inform. Sci. Sys., The Johns Hopkins Univ., Baltimore, MD, Root locations of an entire polytope of polynomials: It suffices to check the edges," in Proc. Amer. Contr. Conf., Minneapolis, MN, 1987. L. X. Xin, "Necessary and sufficient conditions for stability of a class of interval matrices," Int. J. Cont., vol. 45, no. I , pp. 211-214, 1987. [IO] B. R. Barmish and C . L. DeMarco, "A new method for improvement of robustness bounds for linear state equations," in Proc. Conf. Inform. Sci. Syst., Princeton Univ, Princeton, NJ, 1986. S . Bialas, "A necessary and sufficient condition for stability of interval matrices," Int. J. Conir., vol. 37, no. 4, pp. 717-722, 1983. B. R. Barmish and C. V. Hollot, "Counterexample to a recent result on the stability of interval matrices by S. Bialas," Ini. J. Cont., vol. 39, no. 5. pp. 1103-1 104, 1984. "A necessary and sufficient condition for the stability of convex combinations of stable polynomials or matrices," Bull. Polish Acad.Abstract-Polytopes of (characteristic) polynomials arise when systems experience real parameter variations. This paper presents a necessary and sufficient condition (requiring only a finite number of computations) for

A new way to stabilize discrete-time plants under compact uncertainty

“…is used, then the inequality ~t(K) <_ 0 is always solvable and the recurrent algorithm (5) in which the zeros ut_ 1 and u+l of the function ~ot(K) are defined by the relations…”

“…The control problem for uncertain plants has been analyzed, in particular by [1], [2], [3], [4], [5], [6]. Still, no generally applicable methods of stabilizing descrete-time plants under a compact (interval) uncertainty have been developed because in a discrete-time system an arbitrary perturbation cannot be essentially compensated on the knowledge of a priori estimates and because the conventional identification methods do not work if only estimates of exogenous perturbations are available.…”

Chaos and Dynamics Induced by the Amplitude of Load Torque: Analysis and Control

“…e PMSM offers high-performance drive when uses torques due the magnets and reluctance variation; note that the machine has a problem of high speed [2]. e dynamics characteristics, speed control, and oscillations of different types of motor and generator are studies since references [3][4][5][6][7][8][9]. Recently, literature works have been focused on non-nonlinear phenomena arising in PMSM electrical machine [10][11][12][13].…”