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THE RELATIONSHIP BETWEEN GAP METRIC AND time-varying GAP METRIC FOR linear time-varying systemS

INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2013年第5期9卷 2125-2141页

作者： Gong, Ting Lu, Yufeng Dalian Univ Technol Sch Math Sci 2 Linggong Rd Dalian 116024 Peoples R China

This paper is concerned with the relationship between the gap metric and the time-varying gap metric for linear time-varying systems in the feedback configuration. It is shown that these two kinds of gaps are identical to each other when we measure the distance between corresponding graphs of a plant and a controller in a feedback system. This result supplies a simple way for computing the supremum appearing in the definition of the time-varying gap. Furthermore, the developed criteria are also applied to compute the optimal minimal angles of stabilizable linear time-varying systems.

关键词： linear time-varying system Stabilization Gap metric time-varying gap metric Optimal minimal angle

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Application of the least squares algorithm to the observer design for linear time-varying systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1999年第9期44卷 1742-1745页

作者： Chen, MS Yen, JY Natl Taiwan Univ Dept Mech Engn Taipei 10764 Taiwan

In this paper, it is shown that the least squares algorithm with covariance reset, which is originally developed for the purpose of constant parameter identification, can be effectively applied to the observer design for a general linear time-varging system. The new observer successfully avoids many of the disadvantages of other time-varying observers, such as slow convergence rate, heavy computation load, high amplification of measurement noise, and the inapplicability to systems with time-varying observability indexes or discontinuous parameter variations.

关键词： least squares algorithm linear time-varying system observer persistent excitation uniform observability

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H-INFINITY CONTROL OF linear time-varying systemS - A STATE-SPACE APPROACH

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1991年第6期29卷 1394-1413页

作者： RAVI, R NAGPAL, KM KHARGONEKAR, PP UNIV MINNESOTA DEPT ELECT ENGNMINNEAPOLISMN 55455 UNIV MICHIGAN DEPT ELECT ENGN & COMP SCIANN ARBORMI 48109

In this paper the standard problem of H(infinity) control theory for finite-dimensional linear time-varying continuous-time plants is considered. The problem is: given a real number-gamma > 0, find (if one exists) an internally stabilizing controller such that the closed-loop operator norm is less than gamma. Under rather weak assumptions on the plant model, it is shown that a solution to this problem exists if and only if a pair of matrix Riccati differential equations admits positive semidefinite stabilizing solutions. State-space formulae for one solution to the problem are also given.

关键词： H-INFINITY CONTROL THEORY linear time-varying system RICCATI DIFFERENTIAL EQUATIONS OPTIMAL CONTROL

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Robust adaptive pole placement for linear time-varying systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1996年第5期41卷 714-719页

作者： Li, Y Chen, HF ACAD SINICA INST SYST SCIBEIJING 100080PEOPLES R CHINA

This paper studies the robustness properties of a basic adaptive control algorithm with respect to plant parameter variation as well as modeling errors and bounded disturbances. The algorithm consists of a projected gradient estimator and a pole assignment controller, A unified method of proof is presented for robust stability of both discrete and continuous-time adaptively controlled time-varying systems, The robust performance of an adaptive pole assignment controller is also discussed.

关键词： Robust stability pole assignment Controllers device parameter linear time-varying system Self tuning

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QFT parameter-scheduling control design for linear time-varying systems based on RBF networks

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KSME INTERNATIONAL JOURNAL 2003年第4期17卷 484-491页

作者： Choi, JW Yoo, WS Lee, S Im, KH Choi, JY Pusan Natl Univ Sch Mech Engn Pusan 609735 South Korea Pusan Natl Univ Res Inst Mech Technol Pusan 609735 South Korea Seoul Natl Univ Sch Elect Engn & Comp Sci Seoul 151742 South Korea

For most of linear time-varying (LTV) systems, it is difficult to design time-varying controllers in analytic way. Accordingly, by approximating LTV systems as uncertain linear time-invariant, control design approaches such as robust control have been applied to the resulting uncertain LTI systems. In particular, a robust control method such as quantitative feedback theory (QFT) has an advantage of guaranteeing the frozen-time stability and the performance specification against plant parameter uncertainties. However, if these methods are applied to the approximated linear time-invariant (LTI) plants with large uncertainty, the resulting control law becomes complicated and also may not become ineffective with faster dynamic behavior. In this paper, as a method to enhance the fast dynamic performance of LTV systems with bounded time-varying parameters, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks.

关键词： QFT (quantitative feedback theory) linear time-varying system parameter scheduling RBF(radial basis function) network

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On Functional Observers for linear time-varying systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2013年第5期58卷 1354-1360页

作者： Rotella, Frederic Zambettakis, Irene Ecole Natl Ingenieurs Tarbes Lab Genie Prod F-65016 Tarbes France

The technical note deals with existence conditions of a functional observer for linear time-varying systems in the case where the order of the observer is equal to the number of observed variables. Constructive procedures for the design of such a linear functional observer are deduced from the existence conditions. As a specific feature, the proposed procedures do not require the solution of a differential Sylvester equation. Some examples illustrate the presented results.

关键词： Functional observer linear time-varying system Luenberger observer

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A new model reference adaptive control for linear time-varying systems

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2000年第4期14卷 469-479页

作者： Chen, MS Wu, JM Natl Taiwan Univ Dept Mech Engn Taipei 106 Taiwan

Recent results on the adaptive control of linear time-varying systems have considered mostly the case in which the range or rate of parameter variations is small. In this paper, a new state feed-back model reference adaptive control is developed for systems with bounded arbitrary parameter variations. The important feature of the proposed adaptive control is an uncertainty estimation algorithm, which guarantees almost zero tracking error. Note that the conventional parameter estimation algorithm in the adaptive control guarantees only bounded tracking error. Copyright (C) 2000 John Wiley & Sons, Ltd.

关键词： linear time-varying system model reference adaptive control tracking control uncertainty estimation

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Generalization of the Concept of Pole-zero Cancellation to linear time-varying systems 57

Generalization of the Concept of Pole-zero Cancellation to L...

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57th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE)

作者： Kondo, Shingo Jikuya, Ichiro Kanazawa Univ Grad Sch Nat Sci & Technol Kanazawa Ishikawa Japan Kanazawa Univ Fac Elect & Comp Engn Kanazawa Ishikawa Japan

ISBN: (纸本)9784907764609

Pole-zero cancellation is a well-known and important concept in linear time-invariant systems. In contrast, transfer functions as well as poles and zeros are not defined for linear time-varying systems. In this paper, we make an attempt to generalize the concept of pole-zero cancellation to linear time-varying systems. We firstly introduce the new concept of extended transfer function for linear time-varying systems in the time domain instead of the frequency domain. We then propose the computational procedure of pole-zero cancellation to linear time-varying systems. We finally discuss the meaning of the proposed computational procedure regardless of the lack of poles and zeros in linear time-varying systems. The proposed concept and computational procedure are illustrated by a numerical example.

关键词： pole-zero cancellation linear time-varying system Kalman canonical decomposition minimal realization companion form

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Guaranteed error bounds for model reduction of linear time-varying systems

Guaranteed error bounds for model reduction of linear time-v...

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American Control Conference

作者： Lall, S Beck, C Dullerud, G CALTECH Pasadena CA 91125 USA

ISBN: (纸本)0780345304

New techniques are presented for the model reduction of linear time-varying and linear periodically-varying systems, including the formulation and proof of guaranteed upper bounds for the error. The commonly used method of balanced truncation for linear time-invariant systems is generalized to the time-varying case with explicit error bounds that are derived based on generalizations of the 'twice-the-sum-of-the-tail' formula. The development of these reduction results for time-varying systems relies on a new operator framework for analysis of linear time-varying systems, presented in [4], in combination with the model reduction methods for uncertain systems developed in [3].

关键词： Reduced order model linear time-varying system time varying REDUCTION METHODS time invariant systems time-varying systems Bound Upper bound uncertain systems

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On the uniform finite-time stability of continuous linear time-varying systems: A numerical algorithm 37

On the uniform finite-time stability of continuous linear ti...

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37th Chinese Control Conference (CCC)

作者： Chen, Zhihua Xie, Yongchun Beijing Inst Control Engn Beijing 100190 Peoples R China Sci & Technol Space Intelligent Control Lab Beijing 100190 Peoples R China Tianjin Key Lab Micrograv & Hypograv Environm Sim Tianjin 300301 Peoples R China

ISBN: (纸本)9789881563958

The paper deals with the uniform finite-time stability (UFTS) of continuous linear time-varying (LTV) systems. Firstly, a necessary and sufficient condition for the UFTS of continuous LTV systems is devised with the idea of computing the envelope of all the trajectories of the considered system. Then, a corollary is obtained under the perspective of numerical computation. Further, based on the obtained corollary, a novel numerical algorithm is designed by utilizing the Lipschitz continuity of certain functions. With the proposed algorithm, only limited numerical computation is needed when analyzing the UFTS of continuous LTV systems. Compared with the existing Lyapunov-like function method, one needn't constructing Lyapunov-like functions. Moreover, the obtained corollary just requires being checked at a limited number of time points. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the proposed results.

关键词： linear time-varying system Uniform Finite-time stability Numerical algorithm

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