• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.165-180
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• 2017

In this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.209-209
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• 2000

In this paper, we show that some of 2- or higher-dimensional systems cannot be asymptotically stabilized on the constrained asymptotically stabilizable set via linear feedback.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.117-128
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• 1996

Complementation theory in krein spaces can be extended for any self-adjoint transformation. There is a close relation between Julia operators and linear systems. The theory of Julia operators can be used to construct distinct Krein spaces which are the state spaces of extended canonical linear systems with given transfer function.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.571-574
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• 2005

This paper gives some sufficient conditions for a given polyhedral set which is represented as a set of linear inequalities to be positive D-invariant for uncertain linear discrete-time systems in the case such that the systems matrices depend linearly on uncertain parameters whose ranges are given intervals. Further, the results will be applied to uncertain linear continuous systems in the sense of the above by using Euler approximation.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.6
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• pp.641-646
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• 1999

This paper deals with the robust stability of discrete-time linear systems with time- varying delays and norm-bounded uncertainties. In this paper, the magnitude of time-varying delays is assumed to be upper-bounded. The sufficient condition is presented in terms of linear matrix inequality. It is also shown that the robust stability of uncertain discrete-time linear systems with time-varying delays is related with the quadratic stability of uncertain discrete-time linear systems with constant time delay.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.4
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• pp.244-247
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• 2000

In this paper, a discrete-time sliding mode controller for linear time-varying systems with disturbances is proposed. The proposed method guarantees the systems state is globally uniformly ultimately bounded(G.U.U.B) under the existence of time-varying disturbances.

• International Journal of Control, Automation, and Systems
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• v.3 no.4
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• pp.580-590
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• 2005

In this paper, we propose a new stability criterion and a controller design method for switched linear systems. The proposed stability criterion is applicable to each subsystem independently without the need to consider the overall system. The controller can be easily designed through geometric relations between eigenvalues of each subsystem matrix. The proposed methods provide a systematic and simple pole assignment approach for switched linear systems. Illustrative examples are given.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.5
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• pp.351-356
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• 2002

This papaer deals with a model reduction problem for linear systems with time varying parameters. For this problem, a controllability Grammian and an observability Grammian are introduced and computed by solving linear matrix inequalities. Using the controllability/observability Grammian, a balanced state space realization for linear parameter varying systems is obtained. From the balanced state space realization, a reduced model can be obtained by truncating not only states but also time varying parameters and an upper bound of the model reduction error is derived as well.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.121-128
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• 2000

The scope of this paper is focused to the systems which have the time period and they should be necessarily studied in the sense of stability and design method of controller to stabilize the orignal unstable systems. In general, the time periodic systems or the systems having same motions during certain time interval are easily found in rotating motion device, i.e., satellite or helicopter and widely used in factory automation systems. The characteristics of the selected dynamic systems are analyzed with the new stability concept and stabilization control method based on Lyapunov direct method. The new method from Lyapunov stability criteria which satisfies the energy convergence is studied with linear algebraic method. And the numerical procedures are developed with computational programming method to apply to the practical linear periodic systems. The results from this paper demonstrate the usefulness in analysis of the asymptotic stability and stabilization of the unstable linear periodic system by using the developed simulation procedures.