• Journal of Institute of Control, Robotics and Systems
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• v.3 no.1
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• pp.17-22
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• 1997

The stability robustness problem of linear discrete-time systems with time-varying perturbations is considered. By using Lyapunov direct method, the perturbation bounds for guaranteeing the quadratic stability of the uncertain systems are derived. In the previous results, the perturbation bounds are derived by the quadratic equation stemmed from Lyapunov method. In this paper, the bounds are obtained by a numerical optimization technique. Linear matrix inequalities are proposed to compute the perturbation bounds. It is demonstrated that the suggested bound is less conservative for the uncertain systems with unstructured perturbations and seems to be maximal in many examples. Furthermore, the suggested bound is shown to be maximal for the special classes of structured perturbations.

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.89-102
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• 2010

This paper concerns the problem of global robust stability of a time-delay discontinuous system with a positive-defined connection matrix under polytopic-type uncertainty. In order to give the stability condition, we firstly address the existence of solution and equilibrium point based on the properties of M-matrix, Lyapunov-like approach and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. Second, we give the delay-independent and delay-dependent stability condition in terms of linear matrix inequalities (LMIs), and based on Lyapunov function and the properties of the convex sets. One numerical example demonstrate the validity of the proposed criteria.

• Smart Structures and Systems
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• v.21 no.2
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• pp.187-194
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• 2018

This paper focuses on the $H_{\infty}$ filter design problem for offshore steel jacket platforms. Its objective is to design a full-order state observer for offshore platforms in presence of unknown disturbances. To make the method more practical, it is assumed that the measured variables are available at discrete-time instants with time-varying sampling time intervals. By modelling the sampling intervals as a bounded time-varying delay, the estimation error system is expressed as a time-delay system. As a result, the addressed problem can be transformed to the problem of stability of dynamic error between the system and the state estimator. Then, based on the Lyapunov-Krasovskii Functional (LKF), a stability criterion is obtained in the form of Linear Matrix Inequalities (LMIs). According to the stability criterion, a sufficient condition on designing the state estimator gain is obtained. In the end, the proposed method is applied to an offshore platform to show its effectiveness.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.11
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• pp.2103-2108
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• 2011

In this paper, the problem of passivity analysis for neural networks with time-varying delays and norm-bounded parameter uncertainties is considered. By constructing a new augmented Lyapunov functional, a new delay-dependent passivity criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical example are included to show the effectiveness of proposed criterion.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.2
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• pp.376-382
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• 2011

This paper proposes delay-dependent stability conditions of the fuzzy Markovian jumping Hopfield neural networks of neutral type with time-varying delays. By constructing a suitable Lyapunov-Krasovskii's (L-K) functional and utilizing Finsler's lemma, new delay-dependent stability criteria for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. A numerical example is given to illustrate the effectiveness of the proposed methods.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.9
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• pp.1809-1814
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• 2009

In this paper, the problem of stability analysis for neural networks with discrete and distributed time-varying delays is considered. By constructing a new Lyapunov functional, a new delay-dependent stability criterion for the network is established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical example are included to show the effectiveness of proposed criterion.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.137-140
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• 2001

In this paper, we design 75(Takagi-Sugeno) fuzzy controllers for the systems that can be represented by the 75 fuzzy model. We use inverse optimal approach in which the cost function is determined later than the Lyapunov function and its corresponding control input satisfying the design requirements such as stability and decay rate. The obtained design procedure is in the form of solving LMI(Linear Matrix Inequalities), thus very efficient in practice.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.469-471
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• 1999

In this paper, a dynamic output feedback controller design technique for robust decentralized stabilization of uncertain large-scale systems is presented. Based on the Lyapunov method, a sufficient condition for robust stability, is derived in terms of three linear matrix inequalities(LMIs). The solutions of the LMIs can be easily obtained using efficient convex optimization techniques.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.68.5-68
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• 2001

This paper investigates the problem of linear parameter-dependent output feedback controllers design for interconnected linear parameter-varying(LPV) plant. By using a parameter-independent common Lyapunov function, sucient conditions for solving the problems are established, which allow us to design linear parameter dependent decentralized controllers in terms of scaled H-infinite control problems for related linear systems without interconnections. The solvability conditions are expressed in terms of finite-dimensional linear matrix inequalities(LMI´s) evaluated at the extreme points of the admissible parameter set.

• International Journal of Control, Automation, and Systems
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• v.2 no.2
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• pp.182-188
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• 2004

This paper presents a design method of delay-dependent control for T-S fuzzy systems with time delays. Based on parallel distributed compensation (PDC) and a descriptor model transformation of the system, a delay-dependent control is utilized. An appropriate Lyapunov-Krasovskii functional is chosen for delay-dependent stability analysis. A sufficient condition for delay-dependent control is represented in terms of linear matrix inequalities (LMIs).