Showing papers on "Aizerman's conjecture published in 1998"
16 Dec 1998
TL;DR: In this article, the robust stability condition for continuous-time and discrete-time systems with sector nonlinearity is defined and analyzed in terms of the nonlinear allowable band (sector) and the linear allowable gain band (interval set).
Abstract: The robust stability condition for sampled-data control systems with sector nonlinearity was presented in our previous papers (1996,1998) Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system can belong to this type of class The criterion contains the robust stability condition in regard to the nonlinear allowable band (sector) for continuous-time systems and the linear allowable gain band (interval set) for discrete-time systems This paper focuses primarily on robust stability in order to analyze a nonlinear element by the linear gain band, in other words, the validity of the Aizerman conjecture extended into discrete-time systems
19 citations
TL;DR: In this paper, it was proved that non-linear systems with positive impulse functions satisfy the Aizerman conjecture in the input-output version of the problem, and the stability criteria were formulated in terms of the Hurwitzness of corresponding polynomials.
Abstract: It is proved that non-linear systems with positive impulse functions satisfy the Aizerman conjecture in the input–output version. Besides, the stability criteria are formulated in the terms of the Hurwitzness of corresponding polynomials. In addition, new positivity conditions for impulse functions are proposed. © 1998 John Wiley & Sons, Ltd.
3 citations
01 Sep 1998
TL;DR: In this paper, the robust stability condition for continuous-time and discrete-time control systems with sector nonlinearity is defined. But the robustness condition is not applicable to the continuous time systems.
Abstract: The robust stability criterion for sampled-data control systems with a sector nonlinearity was presented in our previous papers (1996, 1998). Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system belongs to this type of class. The criterion contains the robust stability condition in regard to the nonlinear allowable band (sector) for continuous-time systems and the linear allowable gain band (interval set) for discrete-time systems. The paper focuses primarily on the concept of robust stability in order to analyze a nonlinear element by the linear gain band, in other words, the validity of Aizerman's conjecture extended into discrete-time systems.
1 citations
01 Jan 1998
TL;DR: In this article, the robust stability condition for sampled-data control systems with sector nonlinearity was presented, which is applicable only to the sampled data control system of a certain class, and a usual discrete-time control system can belong to this type of class.
Abstract: The robust stability condition for sampled-data control systems with sector nonlinearity was presented in our previous paper. Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system can belongs to this type of class. The criterion contains the robust stability condition in regard to the nonlinear allowable band (sector) for continuous-time systems and the linear allowable gain band (interval set) for discrete-time systems. This paper focuses primarily on robust stability in order to analyze a nonlinear element by the linear gain band, in other words, the validity of the Aizerman coiijecture ex tended in tlo discret e-t i me systems.