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Characterisation of nonlinear and linear time-varying systems by Laplace transformation

INTERNATIONAL JOURNAL OF systemS SCIENCE 2013年第8期44卷 1450-1467页

作者： Erfani, Shervin Bayan, Nima Univ Windsor Dept Elect & Comp Engn Windsor ON N9B 3P4 Canada B Braun Med Inc Irvine CA 92614 USA

In this article we elaborate on various characterisations of nonlinear systems. Specifically, we focus on the frequency-domain characterisation of the class of single-input single-output (SISO) linear time-varying (LTV) systems. We use the model introduced by Wiener using Volterra functional and later elaborated by others. The application of the multidimensional Laplace transform (MDLT) method as a fundamental tool in analysing variable systems and understanding system dynamic behaviours is emphasised. In particular, applications of double or two-dimensional Laplace transform (2DLT) for the analysis and synthesis of LTV circuits and systems are detailed. Examples worked out that illustrate the method and demonstrate its validity in the frequency-domain.

关键词： system characterisation time-invariant nonlinear system linear time-varying system multi-dimensional transfer function nonlinear transformation frequency-response characterisation double Laplace transform two-dimensional Laplace transform (2DLT) multidimensional Laplace transform (MDLT)

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Reducibility of linear time-varying systems of Special Form with Control and Measurements

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JOURNAL OF COMPUTER AND systemS SCIENCES INTERNATIONAL 2019年第1期58卷 1-11页

作者： Kalenova, V. I. Morozov, V. M. Moscow MV Lomonosov State Univ Inst Mech Moscow Russia

This paper considers some classes of linear time-varying systems with control and output vectors that can be reduced to time-invarint systems using a constructive transformation with state-space extension. As an illustrative example, the calibration problem of a gimballess inertial navigation system on a single degree-of-freedom turn table is solved.

关键词： SPECIAL FORM ROTARY TABLE Standing Orders Classes linear time-varying system

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Decoupling and tracking control using eigenstructure assignment for linear time-varying systems

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INTERNATIONAL JOURNAL OF CONTROL 2001年第5期74卷 453-464页

作者： Choi, JW Lee, HC Zhu, JJ Pusan Natl Univ Inst Mech Technol Sch Mech Engn & Res Pusan 609735 South Korea Ohio Univ Sch Elect Engn & Comp Sci Athens OH USA

This work is concerned with the assignment of a desired PD-eigenstructure for linear time-varying systems. Despite its well-known limitations, gain scheduling control appeared to be a focus of the research efforts. Scheduling of frozen-time, frozen-state cont rollers for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, (a) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and then (b) a novel decoupling and tracking control scheme is proposed by using the PD-eigenstructure assignment scheme via a differential Sylvester equation and a Command Generator Tracker for linear time-varying systems. The PD-eigenstructure assignment is utilized as a regulator. A feedforward gain for tracking control is computed by using the command generator tracker. The whole design procedure of the proposed PD-eigenstructure assignment scheme is systematic in nature. The scheme could be used to determine stability of linear time-varying systems easily as well as to provide a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by numerical examples.

关键词： linear time-varying system DECOUPLING eigenstructure assignment tracking control command generator

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Chang Transformation for Decoupling of Singularly Perturbed linear time-varying systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2016年第6期61卷 1637-1642页

作者： Yang, Xiaojing Zhu, J. Jim Beihang Univ Sch Aeronaut Sci & Engn Beijing 100191 Peoples R China Ohio Univ Sch Elect Engn & Comp Sci Athens OH 45701 USA

This technical note extends the decoupling method for singularly perturbed systems, Chang transformation, from linear slowly time-varying systems to linear time-varying systems with semi-proper (self-commutative) fast subsystems through the constructions of contraction mappings when negative real parts of the parallel differential-eigenvalues are used to guarantee the exponential stability of the perturbed systems. MacLaurin series forms and iterative solutions in an interval of the singular perturbation parameter for the differential Riccati equation and the differential Sylvester equation are provided, which are key steps for the Chang transformation construction.

关键词： Chang transformation linear time-varying system semi-proper system singular perturbation

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High-order sliding-mode observer for linear time-varying systems with unknown inputs

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INTERNATIONAL JOURNAL OF ROBUST AND NONlinear CONTROL 2017年第14期27卷 2338-2356页

作者： Galvan-Guerra, R. Fridman, L. Davila, J. Univ Nacl Autonoma Mexico Fac Engn Div Elect Engn Dept Control Engn & Robot Mexico City 04510 DF Mexico IPN Sect Grad Studies & Res ESIME UPT Mexico City 07340 DF Mexico

In this article, an observer for linear time variant systems affected by unknown inputs is suggested. The proposed observer combines the deterministic least squares filter and the high-order sliding-mode differentiator to provide exact state reconstruction in spite of bounded unknown inputs and system instability. The cascade structure of the algorithm provides a correct state reconstruction for the class of linear time variant systems that satisfy the structural property of strong observability. Simulations illustrate the performance of the proposed algorithm. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： sliding modes nonlinear observers uncertain systems linear time-varying system

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Control and Estimation in linear time-varying systems Based on Ellipsoidal Reachability Sets

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AUTOMATION AND REMOTE CONTROL 2020年第8期81卷 1367-1384页

作者： Balandin, D. V. Kogan, M. M. Lobachevsky Nizhny Novgorod State Univ Nizhnii Novgorod Russia Nizhny Novgorod State Univ Architecture & Civil E Nizhnii Novgorod Russia

linear continuous or discrete time-varying systems in which the sum of a quadratic form of the initial state and the integral or sum of quadratic forms of a disturbance on a finite horizon is bounded above by a given value are considered. It is demonstrated that the reachability set of such a continuous- or discrete-time system is an evolving ellipsoid, and its ellipsoid matrix satisfies a linear matrix differential or difference equation, respectively. The optimal ellipsoidal observer and identification algorithm that yield the best ellipsoidal estimates of the system's state and unknown parameters are designed. In addition, the optimal controllers ensuring that the system's state will fall into a target set or that the system's trajectory will stay within the ellipsoidal tube are designed. A connection between the optimal ellipsoidal observer and the Kalman filter is established. Some illustrative examples for the Mathieu equation, which describes the parametric oscillations of a linear oscillator, are given.

关键词： linear time-varying system ellipsoidal reachability set optimal control optimal estimation

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Model-free adaptive fractional order control of stable linear time-varying systems

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ISA TRANSACTIONS 2017年 67卷 193-207页

作者： Yakoub, Z. Amairi, M. Chetoui, M. Saidi, B. Aoun, M. Univ Gabes Natl Engn Sch Gabes Tunisia Res Lab Modeling Anal & Control Syst MACS Gabes Tunisia

This paper presents a new model-free adaptive fractional order control approach for linear time-varying systems. An online algorithm is proposed to determine some frequency characteristics using a selective filtering and to design a fractional PID controller based on the numerical optimization of the frequency domain criterion. When the system parameters are time-varying, the controller is updated to keep the same desired performances. The main advantage of the proposed approach is that the controller design depends only on the measured input and output signals of the process. The effectiveness of the proposed method is assessed through a numerical example. (C) 2017 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： Fractional calculus linear time-varying system Model-free adaptive control Robustness

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Residual generation for fault diagnosis in linear time-varying systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2004年第5期49卷 767-772页

作者： Xu, AP Zhang, QH Shandong Univ Jinan 250100 Peoples R China INRIA IRISA F-35042 Rennes France

A residual generation method for fault diagnosis in deterministic and stochastic linear time-varying systems is proposed in this note. Based on appropriate assumptions on the monitored faults and on some persistent excitation condition, it enables complete diagnosis of any number of faults, regardless of the number of output sensors. In order to generate residuals for fault diagnosis, part of the possible faults are estimated with a recently developed technique of adaptive observer. The sensitivity of the residuals to the monitored faults is rigorously analyzed, as well as their insensitivity to the faults to be ignored.

关键词： adaptive observer fault diagnosis linear time-varying system residual generation

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OBSERVABILITY OF linear time-varying systemS WITH QUASIDERIVATIVE COEFFICIENTS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2019年第3期57卷 1710-1729页

作者： Astrovskii, Anatoly, I Caishun, Ivan, V Belarus State Econ Univ Minsk 220070 BELARUS Natl Acad Sci Belarus Inst Math Minsk 220072 BELARUS

On the basis of quasiderivatives and the upper triangular Hessenberg form, an approach to investigating the observability problem for linear time-varying systems is proposed. The quasiderivatives are defined for some lower triangular matrix, and the simplest rules of the quasidifferentiation are described. Conditions for linear independence of continuous quasidifferentiable functions are established in terms of the Wronski matrix. The necessary and sufficient conditions for an upper triangular Hessenberg form in the orbit of linear time-varying systems are obtained, and the method to find such systems is described. New efficient conditions for various types of observability (complete, differential, uniform) are obtained.

关键词： linear time-varying system observability quasidifferentiation Hessenberg form observability matrix

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Criterion for robustness of global asymptotic stability to external perturbations of linear time-varying systems

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INTERNATIONAL JOURNAL OF GENERAL systemS 2021年第2期50卷 211-222页

作者： Vrabel, R. Slovak Univ Technol Bratislava Inst Appl Informat Automat & Mechatron Trnava Slovakia

In this paper, we establish a new criterion for robustness of global asymptotic stability of zero solution of LTV system (x) over dot = A(t) x in the presence of external perturbations (disturbances). To prove the result, logarithmic norm will be used under which the stability becomes a topological notion depending on the chosen vector norm in the state-space R-n.

关键词： linear time-varying system perturbation robust global asymptotic stability logarithmic norm

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