• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.8
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• pp.1429-1433
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• 2008

In this paper, we consider the design method of robust guaranteed cost controller for discrete-time singular systems with norm-bounded time-varying parameter uncertainty. In order to get the optimum(minimum) value of guaranteed cost, an optimization problem is given by linear matrix inequality (LMI) approach. The sufficient condition for the existence of controller and the upper bound of guaranteed cost function are proposed in terms of strict LMIs without decompositions of system matrices. Numerical examples are provided to show the validity of the presented method.

• Journal of Advanced Navigation Technology
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• v.26 no.6
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• pp.504-509
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• 2022

In this paper, we deal with the stability condition of linear time-varying interval discrete systems with time-varying delays and unstructured uncertainty. For the time-varying interval discrete system which has interval matrix as its system matrices, time-varying delay time within some interval value and unstructured uncertainty which can include non-linearity and be expressed by only its magnitude, the stability condition is proposed. Compared with the previous result derived by using a upper bound solution of the Lyapunov equation, the new result is derived by the form of simple inequality based on Lyapunov stability condition and has the advantage of being more effective in checking stability. Furthermore, the proposed condition is very comprehensive, powerful and inclusive the previously published conditions of various linear discrete systems, and can be expressed by the terms of magnitudes of the time-varying delay time and uncertainty, and bounds of interval matrices. The superiority of the new condition is shown in the derivation, and the usefulness and advantage of the proposed condition are examined through numerical example.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.401-404
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• 1998

In this paper, we present robust reliable $H\infty$ controller design methods of continuous and discrete uncertain time delay systems through LMI(linear matrix inequality) approach, respectively. Also the existence conditions of state feedback control are proposed. Using some changes of varables and Schur complements, the obtained sufficient conditions are transformed into LMI form. We show the validity of the proposed method through numerical examples.

• 전기의세계
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• v.20 no.4
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• pp.17-22
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• 1971

This paper deals with the analytic structure of feedback controller for linear time invariant discrete systems. On the way of developing the deadbeat controller, some necessary conditions for control policy have been derived. In the case of time delay, it was proved that the q periods delay in the control causes q periods delay in the point at which deadbeat response occurs. Theorems and conclusions are illustrated with some simple nontrivial numerical examples and signal state tracking application problems.

• Journal of the Korean Statistical Society
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• v.35 no.3
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• pp.281-303
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• 2006

In an earlier work, we investigated the problem of using linear programming to bound performance measures in a discrete time Jackson network. There it was assumed that the system evolution is controlled by the early arrival scheme. This assumption implies that the system can't be modelled by a Markov chain. This problem was resolved and performance bounds were calculated. In the present work, we use a modification of the early arrival scheme (without corrupting it) in order to make the system evolves as a Markov chain. This modification enables us to obtain explicit expressions for certain moments that could not be calculated explicitly in the pure early arrival scheme setting. Moreover, this feature implies a reduction in the linear program size as well as the computation time. In addition, we obtained tighter bounds than those appeared before due to the new setting.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.31B no.5
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• pp.65-72
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• 1994

We resolve the suboptimal $\infty$ control problem using (J,J')-lossless coprime factorization by transforming the linear fractional transformation (LFT) into chain scattering description (CSD) in discrete-time systems. The condition transformed LFT into CSD is that the inverse matrix of $P_{21}$ of standard plant exists. But, this paper presents the method of transforming LFT into CSD for 4-block problem in case that the inverse matrix of $P_{21}$ of standard plant does not exist and parameterization of the all suboptimal $\infty$T controllers using (J,J')-lossless coprime factorization. It is shown that this method can resolve the suboptimal $\infty$ control problem solving only two Riccati equations in discrete-time systems.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.865-871
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• 2009

In this paper, a novel feedback linearization is proposed for discrete-time nonlinear systems described by discrete-time T-S fuzzy models. The local linear models of a T-S fuzzy model are transformed to a controllable canonical form respectively, and their T-S fuzzy combination results in a feedback linearizable Tagaki-Sugeno fuzzy model. Based on this model, a nonlinear state feedback linearizing input is determined. Nonlinear state transformation is inferred from the linear state transformations for the controllable canonical forms. The proposed method of this paper is more intuitive and easier to understand mathematically compared to the well-known feedback linearization technique which requires a profound mathematical background. The feedback linearizable condition of this paper is also weakened compared to the conventional feedback linearization. This means that larger class of nonlinear systems is linearizable compared to the case of classical linearization.

• ETRI Journal
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• v.18 no.3
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• pp.127-145
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• 1996

A new analytic framework based on a linear algebra approach is proposed for examining the performance of a direct sequence spread spectrum (DS/SS) slotted ALOHA wireless communication network systems with delay capture. The discrete-time Markov chain model has been introduced to account for the effect of randomized time of arrival (TOA) at the central receiver and determine the evolution of the finite population network performance in a single-hop environment. The proposed linear algebra approach applied to the given Markov problem requires only computing the eigenvector ${\prod}$ of the state transition matrix and then normalizing it to have the sum of its entries equal to 1. MATLAB computation results show that systems employing discrete TOA randomization and delay capture significantly improves throughput-delay performance and the employed analysis approach is quite easily and staightforwardly applicable to the current analysis problem.

• International Journal of Control, Automation, and Systems
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• v.2 no.4
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• pp.501-508
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• 2004

A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N-th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed for a discrete state delay system whose state delay is not exactly known but only known to lie in a certain interval.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2516-2518
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• 2004

This paper proposes a stability condition in discrete-time affine Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and then, introduces the design method of a fuzzy-model-based controller which guarantees the stability. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The search for a piecewise quadratic Lyapunov function can be represented in terms of linear matrix inequalities (LMIs).