Implicit and Descriptor Systems

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Author Index
A B C D E F G H I
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Stability And Stabilization Of Implicit Systems

Authors:

Izumi Masubuchi,

Volume: 1, Page 3636 Paper number 127

Abstract:

This paper is concerned with stability and stabilization of implicit systems. Stability criteria are provided in terms of the Kronecker form, Lyapunov equation and inequality and conditions on extended rank and invertibility of the system pencil. Then stabilization of implicit systems via interconnection is considered based on the notion of initial-freedom preservation as a formulation of regularity of interconnection. To analyze stabilization with initial-freedom preservation, we define complete-stabilizability and zero-detectability. It is shown that stabilizability via interconnection with initial-freedom preservation is equivalent to complete-stabilizability and zero-detectability. Thus standard results on output feedback stabilization of state-space and descriptor systems are generalized to stabilization of implicit systems via interconnection.

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More About Non Square Implicit Descriptions For Modelling And Control

Authors:

Moisés Bonilla-Estrada, Michel Malabre,

Volume: 1, Page 3642 Paper number 1323

Abstract:

We extend here some of our previous results on non square implicit descriptions which can be used for modelling broader classes of linear systems, for instance systems with internal switches. We introduce ladder systems, for which, though the input-output behaviour can vary from a first order to nth order system (depending on the position of the internal switches), the non square (flat) implicit description is unique. When some conditions are satisfied (on the basis some of our previous results), it is possible to control such an implicit system so that it behaves as a pre-specified model. Our presentation here is mainly oriented towards modelling, with a particular example extracted from agronomical applications.

CD001323.PDF (From Author) CD001323.PDF (Scanned)

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A New Algorithm for Solving Cross-Coupled Algebraic Riccati Equations of Singularly Perturbed Nash Games

Authors:

Hiroaki Mukaidani, Hua Xu, Koichi Mizukami,

Volume: 1, Page 3648 Paper number 8021

Abstract:

In this paper, we study the linear quadratic Nash games for infinite horizon singularly perturbed systems. In order to solve the problem, we must solve a pair of cross-coupled algebraic Riccati equations with a small positive parameter. As a matter of fact, we propose a new algorithm, which combines Lyapunov iterations and the generalized Lyapunov equation direct method, to solve the cross-coupled algebraic Riccati equations. The new algorithm ensures that the solution of the cross-coupled algebraic Riccati equations converges to a positive semidefinite stabilizing solution. Furthermore, in order to solve the cross-coupled algebraic Riccati equations, we propose a new Riccati iterations method different from existing method. As another important feature of this paper, our method is applicable to both standard and nonstandard singularly perturbed systems.

CD008021.PDF (From Author)

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Asymptotic Behaviour of the Norm of Input-Output Operators Corresponding to Singularly Perturbed Systems with Multiplicative White Noise

Authors:

Vasile Dragan, Toader Morozan, Peng Shi,

Volume: 1, Page 3654 Paper number 1582

Abstract:

In this paper, we study the problem of asymptotic property of the norm of input-output operators related to a class of singularly perturbed stochastic linear systems. The system is under perturbation of multiplicative white noise. By using reduction order and boundary layer techniques, it is shown that the norm of the operator of the perturbed system is less than a given number (gamma) when the small perturbation (varepsilon) tends to zero, if both the related norms of the reduced subsystem and the boundary layer subsystem are less than (gamma).

CD001582.PDF (From Author)

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Disturbance Decoupling In Descriptor Systems Via Output Feedback ---A Parametric Eigenstructure Assignment Approach

Authors:

G.R. Duan, G.P. Liu, S. Thompson,

Volume: 1, Page 3660 Paper number 1724

Abstract:

Based on a recently proposed complete parametric approach for eigenstructure assignment in descriptor linear systems via output feedback, disturbance decoupling using output feedback in descriptor linear systems is investigated. Both the dynamical and static disturbance decoupling problems are tackled. Necessary and sufficient conditions for both problems are proposed in terms of the closed-loop eigenvalues and eigenvectors. By arranging these conditions into constraints on the design parameters provided by eigenstructure assignment, the disturbance decoupling problems are converted into eigenstructure assignment problems with extra parameter constraints. The approach guarantees closed-loop regularity, offers certain flexibility and can provide all the degrees of design freedom. An example is investigated to show the effect of the proposed approach.

CD001724.PDF (From Author)

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Strictly Positive Real Lemma for Discrete-Time Descriptor Systems

Authors:

Li Lee, Jian Liung Chen,

Volume: 1, Page 3666 Paper number 1435

Abstract:

In this paper, the strictly positive real (SPR) lemma for discrete-time descriptor systems is addressed. The relationship between strict positive realness and bounded realness (BR) of transfer matrices for such systems is developed. Based on this development, an LMI-based necessary and sufficient condition for a descriptor system being admissible and simultaneously SPR is established.

CD001435.PDF (From Author)

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Anticipation Of Linear Systems With State - Feedbacks

Authors:

Tadeusz Kaczorek,

Volume: 1, Page 3668 Paper number 1010

Abstract:

The concepts of anticipatory discrete-time and continuous-time systems for singular linear systems are introduced. Necessary and sufficient conditions for anticipation of the linear systems are established. It is shown that the anticipation of singular systems is not invariant under state-feedbacks. A procedure is presented for a suitable choice of state feedback for anticipatory (not anticipatory) system such that the closed loop system is not anticipatory (is anticipatory).

CD001010.PDF (From Author)

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