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Improvement of the ARE Strict Bounded Real lemma

Improvement of the ARE Strict Bounded Real Lemma

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2009中国控制与决策会议

作者： Yiping Cheng School of Electronic and Information Engineering Beijing Jiaotong University,Beijing 100044,China

The existing ARE version of the strict bounded real lemma,which establishes equivalence between a strict H norm bound condition and the existence of a positive semidefinite stabilizing solution of an ARE,comes with an a priori stability hypothesis which makes its use cumbersome.This paper proposes an improved version of the lemma where the stability condition is not as a hypothesis but instead goes with the norm bound condition.The improved version offers nothing less than the existing one while providing additionally the fact that the stability is already ensured by the fulfilment of the ARE condition.Similar improvements are also done to the positive real lemma and the L version of the bounded/positive real lemma.

关键词： Bounded real lemma Positive real lemma kyp lemma Algebraic Riccati equations

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Global convergence of a class of nonlinear dynamical networks

Global convergence of a class of nonlinear dynamical network...

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第26届中国控制与决策会议

作者： Ao Dun Di Liang Haijing Liu Electronic Information and Control Engineering Beijing University of Technology

This paper considers the global convergence of a class of nonlinear dynamical networks, and the subsystems are discrete time pendulum-like systems. Different from most of the existing results, two kinds of interconnections are considered in view of the fact that the subsystems of networks may have more than one kind of interconnection between each other. The Kalman-Yakubovich-Popov（kyp） lemma and the Schur complement formula are applied to get novel criteria, which have the forms of linear matrix inequalities（LMIs）. The Kronecker product is presented which can be used to handle a class of LMI problems. The test of the global convergence of a network of pendulum-like systems is separated into the test of the global convergence of several independent pendulum-like systems. Furthermore, a controller design method based on LMIs is provided. Finally, a numerical example is presented to illustrate the efficiency and applicability of the proposed methods.

关键词： Global convergence Nonlinear networks Pendulum-like systems kyp lemma Kronecker product

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Rich Global Dynamical Phenomenon of a Synchronous Machine Model

Rich Global Dynamical Phenomenon of a Synchronous Machine Mo...

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第三十届中国控制会议

作者： LU Pingli~1,YANG Ying~(*2) 1.School of Automation,Beijing Institute of Technology,Beijing 100081,P.R.China 2.Department of Mechanics and Aerospace Engineering,Peking University,Beijing 100871,P.R.China

In this paper,rich global dynamical properties are considered for a fundamental synchronous machine model:from global asymptotic stability of trivial equilibrium to chaotic oscillations.Based on Kalman-Yakubovich-Popov(kyp) lemma, static feedback controller is designed such that the synchronous machine model is global asymptotic stable which guarantees that the existence of limit cycles or chaotic oscillations is impossible.

关键词： Synchronous machines Gradient-like Chaos kyp lemma

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