Journal ArticleDOI
Guaranteed domains of attraction for multivariable luré systems via open Lyapunov surfaces
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In this article, a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time-invariant system and whose feedback path contains multiple sector-bounded nonlinearities is constructed via open Lyapunov surfaces.Abstract:
SUMMARY In this paper we provide guaranteed stability regions for multivariable Lure« -type systems. Specifically, using the Lure« —Postnikov Lyapunov function a guaranteed subset of the domain of attraction for a feedback system whose forward path contains a dynamic linear time-invariant system and whose feedback path contains multiple sector-bounded time-invariant memoryless nonlinearities is constructed via open Lyapunov surfaces. It is shown that the use of open Lyapunov surfaces yields a considerable improvement over closed Lyapunov surfaces in estimating the domain of attraction of the zero solution of the nonlinear system. An immediate application of this result is the computation of transient stability regions for multimachine power systems and computation of stability regions of anti-windup controllers for systems subject to input saturation. ( 1997 by John Wiley & Sons, Ltd.read more
Citations
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Journal ArticleDOI
Absolute stability with a generalized sector condition
Tingshu Hu,Bin Huang,Zongli Lin +2 more
TL;DR: This paper generalizes the linear sector in the classical absolute stability theory to a sector bounded by concave/convex functions, allowing more flexible or more specific description of the nonlinearity and will thus reduce the conservatism in the estimation of the domain of attraction.
Journal ArticleDOI
An LQR/LQG theory for systems with saturating actuators
TL;DR: It is shown that SLQR/SLQG controllers ensure semi-global stability by appropriate choice of a parameter in the performance criterion by using the stochastic linearized system and the Lagrange multiplier technique.
Journal ArticleDOI
A Transient Stability Assessment Framework in Power Electronic-Interfaced Distribution Systems
Yun Zhang,Le Xie +1 more
TL;DR: In this article, a framework of transient stability assessment for future distribution systems that are comprised of multiple micro-grids is introduced, where an angle droop method is introduced for autonomous real power sharing among coupling-operated microgrids.
Journal ArticleDOI
Brief paper: Convex invariant sets for discrete-time Lur'e systems
TL;DR: It is proven that the LNL-invariant sets provided by this algorithm are polyhedral convex sets and constitute an estimation of the domain of attraction of the non-linear system.
Journal ArticleDOI
Control of systems with actuator saturation non-linearities: An LMI approach
TL;DR: In this paper, a static, full-state feedback and a dynamic, output feedback control design framework for continuous-time, multivariable, linear, time-invariant systems subject to time invariant, sector-bounded, input nonlinearities is presented.
References
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Book
Nonlinear Systems Analysis
TL;DR: In this article, the authors consider non-linear differential equations with unique solutions, and prove the Kalman-Yacubovitch Lemma and the Frobenius Theorem.
Book
Stability of nonlinear control systems
TL;DR: In this article, Liapunov and Popov developed a control system as developed from direct method of LAPUNOV, noting V. M. Popov's contribution.
Journal ArticleDOI
Paper: Maximal lyapunov functions and domains of attraction for autonomous nonlinear systems
TL;DR: This paper presents various theoretical and computational methods for estimating the domain of attraction of an autonomous nonlinear system based on the concept of a maximal Lyapunov function, which is introduced in this paper.