• Korean Journal of Mathematics
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• v.27 no.2
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• pp.515-523
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• 2019

The aim of this paper is to present some necessary and sufficient conditions for existence of solution of Sylvester operator equation involving bounded subnormal operators in a Hilbert space. Our results improve and generalize some results in the literature involving normal operators.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.7
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• pp.577-582
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• 2013

In this paper Legendre wavelets are used to approximate the solutions of linear time-invariant system. The Legendre wavelet and its integral operational matrix are presented and an efficient algorithm to solve the Sylvester matrix equation is proposed. The algorithm is based on the decomposition of the Sylvester matrix equation and the preorder traversal algorithm. Using the special structure of the Legendre wavelet's integral operational matrix, the full order Sylvester matrix equation can be solved in terms of the solutions of pure algebraic matrix equations, which reduce the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.777-786
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• 1999

This work is concerned with the assignment of the desired eigenstructure for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain scheduling control appeared to be the focus of the research efforts. Scheduling of frozen-time, frozen-state controller 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, ⅰ) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ⅱ) we also propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon the newly developed notions. The whole design procedure of the proposed eigenstructure assignment scheme is very systematic, and the scheme could be used to determine the stability of linear time-varying systems easily as well as provides a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by a numerical example.

• Journal of Institute of Control, Robotics and Systems
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• v.19 no.9
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• pp.827-833
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• 2013

In this paper, an efficient computational method is presented for state space analysis of bilinear systems via Legendre wavelets. The differential matrix equation is converted to a generalized Sylvester matrix equation by using Legendre wavelets as a basis. First, an explicit expression for the inverse of the integral operational matrix of the Legendre wavelets is presented. Then using it, we propose a preorder traversal algorithm to solve the generalized Sylvester matrix equation, which greatly reduces the computation time. Finally the efficiency of the proposed method is discussed using numerical examples.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.12
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• pp.1270-1277
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• 2008

A Haar wavelet based numerical method for solving singularly perturbed linear time invariant system is presented in this paper. The reduced pure slow and pure fast subsystems are obtained by decoupling the singularly perturbed system and differential matrix equations are converted into algebraic Sylvester matrix equations via Haar wavelet technique. The operational matrix of integration and its inverse matrix are utilized to reduce the computational time to the solution of algebraic matrix equations. Finally a numerical example is given to demonstrate the validity and applicability of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.11
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• pp.1621-1628
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• 2004

This paper proposes a design methodology for the robust observer using the eigenstructure assignment in multi-output systems so that the observer is less sensitive to the ill-conditioning factors such as unknown initial estimation error, modeling error and measurement bias in transient and steady-state observer performance. The robustness of the observer can be achieved by selecting the desired eigenvector matrix to have a small condition number that guarantees the small upper bound of the estimation error. So the left singular vectors of the unitary matrix spanned by space of the achievable eigenvectors are selected as a desired eigenvectors. Also, this paper proposes how to select the desired eigenvector based on the measure of observability and designs the observer with small gain. An example of a spindle drive system is simulated to validate the robustness to the ill-conditioning factors in the observer performance.

• International Journal of Control, Automation, and Systems
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• v.5 no.1
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• pp.93-98
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• 2007

A class of new observers in descriptor linear systems, proportional-derivative(PD) observers, are proposed. A parametric design approach for such observers is proposed based on a complete parametric solution to the generalized Sylvester matrix equation. The approach provides complete parameterizations for all the observer gains, gives the parametric expression for the corresponding left eigenvector matrix of the observer system matrix, realizes elimination of impulsive behaviors, and guarantees the regularity of the observer system.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.2
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• pp.145-152
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• 2004

In this paper, an S(stochastic)-eigenvalue and its corresponding S-eigenvector concept for linear continuous-time systems with probabilistic uncertainties are proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the stochastic variable parameters in the dynamic model of a plant. An S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue/-eigenvector concept is also proposed. The proposed control design scheme based on the proposed concept is applied to a longitudinal dynamics of an open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure effects. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on the system.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.7-12
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• 2003

In this paper, S(stochastic)-eigenvalue concept and its S-eigenvector for linear continuous-time systems with probabilistic uncertainties are proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the probabilistic variable parameters in the dynamic model of a plant. S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue concept is also proposed. The proposed design scheme is applied to the longitudinal dynamics of open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure.

• Journal of Mechanical Science and Technology
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• v.18 no.6
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• pp.933-945
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• 2004

In this paper, S (stochastic)-eigenvalue concept and its S-eigenvector for linear continuous-time systems with probabilistic uncertainties is proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the probabilistic variable parameters in the dynamic model of a plant. S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue concept is also proposed. The proposed design schemes are illustrated by numerical examples, and applied to the longitudinal dynamics of open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on S-eigenstructure assignment.