• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.424-427
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• 1995

In this paper, a control law based on the receding horizon concept which robustly stabilizes time-varying discrete linear systems, is proposed. A dynamic game problem minimizing the worst case performance, is adopted as an optimization problem which should be resolved at every current time. The objective of the proposed control law is to guarantee the closed loop stability and the infinite horizon $H^{\infty}$ norm bound. It is shown that the objective can be achieved by selecting the proper terminal weighting matrices which satisfy the inequality conditions proposed in this paper. An example is included to illustrate the results..

• Journal of Advanced Navigation Technology
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• v.18 no.5
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• pp.501-507
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• 2014

A dynamic system is called positive if any trajectory of the system starting from non-negative initial states remains forever non-negative for non-negative controls. In this paper, new sufficient conditions for asymptotic stability of the interval positive time-varying linear discrete-time systems with time-varying delay in states are considered. The considered time-varying delay time has an interval-like bound which has minimum and maximum delay time. The proposed conditions are established by using a solution bound of the Lyapunov equation and they are expressed by simple inequalities which do not require any complex numerical algorithms. An example is given to illustrate that the new conditions are simple and effective in checking stability for interval positive time-varying discrete systems.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.10
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• pp.1287-1292
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• 1999

In large-scale systems, we frequently encounter the time-delay and the uncertainty, and these should be considered in the design of controller because these are the source of the degradation of the system performance and instability of system. In this paper, we consider the robust stability of the linear large scale systems with the uncertainties and the time-delays. The considered uncertainties are both structured uncertainty and the unstructured uncertainty. Also, the considered time-delays are time-varying having finite time derivative limits. Based on the Lyapunov theorem and the linear matrix inequality(LMI) technique, we present two sufficient conditions that guarantee the robust stability of the system. The conditions are expressed as the LMI forms which can be easily checked their feasibility by using the well-known LMI control toolbox. Finally, we show by two examples that our results are less conservative than the previous results.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.293-303
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• 2006

This paper describes a numerical scheme for optimal control of a time-dependent linear system to a moving final state. Discretization of the corresponding differential equations gives rise to a linear algebraic system. Defining some binary variables, we approximate the original problem by a mixed integer linear programming (MILP) problem. Numerical examples show that the resulting method is highly efficient.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.342-345
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• 1996

This paper is dealing with a design of linear controller so that the plant output is regulated to follow a reference model output when the plant equation is described by a class of nonlinear time-varying control systems.

• International Journal of Automotive Technology
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• v.8 no.4
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• pp.445-453
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• 2007

This paper presents a robust controller design approach for improving vehicle dynamic roll motion performance and guaranteeing the closed-loop system stability in spite of vehicle parameter variations resulting from aging elements, loading patterns, and driving conditions, etc. The designed controller is linear parameter-varying (LPV) in terms of the time-varying parameters; its control objective is to minimise the $H_{\infty}$ performance from the steering input to the roll angle while satisfying the closed-loop pole placement constraint such that the optimal dynamic roll motion performance is achieved and robust stability is guaranteed. The sufficient conditions for designing such a controller are given as a finite number of linear matrix inequalities (LMIs). Numerical simulation using the three-degree-of-freedom (3-DOF) yaw-roll vehicle model is presented. It shows that the designed controller can effectively improve the vehicle dynamic roll angle response during J-turn or fishhook maneuver when the vehicle's forward velocity and the roll stiffness are varied significantly.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.4
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• pp.289-294
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• 2011

Digital redesign is yet another efficient tool to convert a pre-designed analog controller into a sampled-data one to maintain the analog closed-loop performance in the sense of state matching. A rising difficulty in developing a digital redesign technique for trackers with time-varying references is the unavailability of a closed-form discrete-time model of a system, even if it is linear time-invariant. A way to resolve this is to approximate the time-varying reference as a piecewise constant one, which deteriorates the state matching performance. Another remedy may be to decrease a sampling period, which however could numerically destabilize the optimization-based digital redesign condition. In this paper, we develop a digital redesign condition for time-varying trackers by approximating the time-varying reference through a triangular hold and by introducing delta-operated discrete-time models. It is shown that the digitally redesigned sampled-data tracker recovers the performance of the pre-designed analog tracker under a fast sampling limit. Simulation results on the formation flying of satellites convincingly show the effectiveness of the development.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.9
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• pp.1796-1801
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• 2009

This paper is concerned with the problem of delay-dependent robust $H_{\infty}$ filtering for uncertain descriptor systems with time-varying delay. The considering uncertainty is convex compact set of polytoic type. The purpose is the design of a linear filter such that the resulting filtering error descriptor system is regular, impulse-free, and asymptotically stable with $H_{\infty}$ norm bound. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) for delayed descriptor systems is derived. Based on the derived BRL, a robust $H_{\infty}$ filter is designed in terms of linear matrix inequaltity (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.41 no.2
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• pp.29-36
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• 2004

This paper deals with a fractional model reduction for linear systems with time varying delayed states. A contractive coprime factorization of linear time delayed systems is defined and obtained by solving linear matrix inequalities. Using generalize controllability and observability gramians of tile contractive coprime factor, a balanced state space realization of the system is derived. The reduced model will be obtained by truncating states in the balanced realization and an upper bound of model approximation error is also presented. In order to demonstrate efficacy of the suggested method, a numerical example is illustrated.

• Journal of Advanced Navigation Technology
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• v.20 no.5
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• pp.475-481
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• 2016

In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.