• Journal of the Korea Institute of Information and Communication Engineering
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• v.6 no.1
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• pp.6-13
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• 2002

This paper deals with the linear matrix inequality (LMI) design procedures for multi-objective Η$_2$/Η$_{\infty}$ controllers with pole-placement constraints for an inverted pendulum system modeled as convex polytopes to ensure the stabilizing regulator and tracking performances. Polytopic models with multiple linear time-invariant models linearized at some operating points are derived to design controllers overcoming the conservativeness such as a controller may have when it is designed for a model linearized at a single operating point. Multi-objective controllers are designed for polytopic models by the LMT design technique with convex algorithms. It is observed that the inverted pendulum controlled by any controller designed for each polytopic model is stabilizingly restored to the vertical angle position for initial values of larger tilt anlges.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.5
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• pp.549-554
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• 2012

In this paper, we consider the optimal fuzzy filter of nonlinear discrete-time with estimation error variance constraint. First, the Takagi and Sugeno(T-S) fuzzy model is employed to approximate the nonlinear system. Next, the error state is mean square bounded, and the steady state variance of the estimation error of each state is not more than the individual predefined value. It is shown that, the addressed problem can be carried out by solving linear matrix inequality(LMI) and some algebraic quadratic matrix inequalities. Finally, some examples are provided to illustrate the design procedure and expected performance through simulations.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.1944-1945
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• 2011

본 논문은 심도각 범위를 고려한 무인 잠수정(autonomous underwater vehicles: AUVs)의 타카키-수게노 (Takagi-Sugeno: T-S) 퍼지 모델 기반 강인 심도 제어기의 설계 기법을 제안한다. 무인 잠수정의 비선형 시스템은 Sector nonlinearity 기법을 이용하여 T-S 퍼지 시스템으로 모델링된다. 리아푸노프(Lyapunov) 함수를 이용하여 무인 잠수정의 성능을 보장하는 선형 행렬 부등식(Linear matrix inequality: LMI) 형태의 강인 제어기 설계 조건은 유도된다. 또한 무인 잠수정의 심도각 범위를 고려하여 입력 및 출력에 제한 조건을 포함한다. 모의 실험을 통해 제안된 기법의 심도 제어 성능을 검증한다.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.111-114
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• 2003

In this paper, we consider the stabilization and $H_\infty$ control of linear systems with static output feedback control. The static output feedback control represents the simplest closed-loop control that can be realized in practice, and, moreover, it is less expensive to be implemented and is more reliable. In spite of its advantages, it is one of the open problems which is not sloved analytically or numerically yet. After decompose the closed-loop system into feedback form, by adopting the small gain theorem, we obtain a sufficient condition for stabilization and a sufficient condition for It control expressed as linear matrix inequalites. Finally, we show the usefulness of our results by a numerical example.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.2
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• pp.95-103
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• 2002

This paper deals with the H$_{\infty}$ control problems for discrete-time linear systems with time-varying delays in states. The existence condition and the design method of the H$_{\infty}$ state feedback controller are given. In this paper, the H$_{\infty}$ control law is assumed to be a memoryless state feedback, and the upper-bound of time-varying delay and S-procedure are used. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.5
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• pp.22-28
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• 2009

In this paper, we consider the problem of $H_{\infty}$ filtering for continuous-time singular systems with multiple state-delays. The aim of designed filter is to guarantee regularity, impulse-free, asymptotic stability and $H_{\infty}$ norm bound of filtering error singular system. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent BRL (bounded real lemma) for singular systems with multiple state-delays is derived. Based on the result, the existence condition of $H_{\infty}$ filter and filter design method are proposed in terms of LMI (linear matrix inequality). Finally, a numerical example is provided to show the validity of the design methods.

• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2642-2644
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• 2000

In this paper, the decoupling $H_{\infty}$ controller which minimizes maximum energy in the output signal is designed to reduce the coupling properties between input/output variables which make it difficult to efficiently control a system. And for a given decoupling $H_{\infty}$ problem, an efficient method is sought to find the controller coefficients through Linear Matrix Inequalities(LMI) by which the problem is formulated into a convex optimal problem.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.38 no.6
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• pp.38-45
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• 2001

In this paper, numerical stability analysis methodology for the singleton-type linguistic fuzzy control systems is proposed. The proposed stability analysis is not the analytical method but the numerical method using the convex optimization of Quadratic Programming (QP) and Linear Matrix Inequalities (LMI). Finally, the applicability of the suggested methodology is highlighted via simulation results.

• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.483-487
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• 2007

This paper is concerned with the observer design problem for linear neutral systems with time-varying delays. The problem addressed is that of designing a full-order observer that guarantees the exponential stability of the error system. An effective algebraic matrix equation approach is developed to solve this problem. In particular, both observer analysis and design problems are investigated. Sufficient conditions for a linear neutral system to be stable are first established. Furthermore, an illustrative example is used to demonstrate the validity of the proposed design procedure.