• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.9
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• pp.1648-1654
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• 2007

In this paper, we consider the design of $H_\infty$ high-gain state feedback control for time-delayed linear systems with limited actuator capacities. The high-gain control means that the control permits the predetermined degree of saturation. Based on new Lyapunov-Krasovskii functional, we derive a result in the form of matrix inequalities. The matrix inequalities are consisted of LMIs those confirm the positive definiteness of Lyapunov- Krasovskii functional, satisfaction of predetermined degree of saturation, reachable set and $L_2$ gain constraint. The result is dependent on the bound of time-delay and its rate, predetermined degree of saturation, actuator capacity, and the allowed size of disturbances. Finally, we give a numerical example to show the effectiveness and usefulness of our result.

• Journal of Electrical Engineering and Technology
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• v.13 no.6
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• pp.2521-2529
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• 2018

This paper deals with a sampled-data tracking control problem for the Takagi-Sugeno fuzzy system with external disturbances. We derive a stability condition guaranteeing both asymptotic stability and H-infinity tracking performance by employing a newly proposed time-dependent line-integral fuzzy Lyapunov-Krasovskii functional. A new integral inequality is also introduced, by which the proposed stability condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed method is demonstrated through a simulation example.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.1
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• pp.127-136
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• 2017

This paper investigates improved stability and stabilization criteria for sampled-data control systems. By using a suitable and newly constructed augmented Lyapunov-Krasovskii functional and some recent mathematic techniques such as auxiliary function-based integral inequalities, sufficient conditions for stability and stabilization conditions are derived within the framework of linear matrix inequalities(LMI) form. The superiority and validity of the proposed results are illustrated by three numerical examples.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.3
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• pp.620-624
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• 2011

This paper propose a new delay-dependent stability criterion of neutral time-delay systems. By employing double-integral terms in augmented states and constructing a new Lyapunov-Krasovskii's functional, a delay-dependent stability criterion is established in terms of Linear Matrix Inequality. Through numerical examples, the validity and improvement results obtained by applying the proposed stability criterion will be shown.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.741-748
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• 2012

In this work, we prove the instability of solutions for a class of nonlinear functional differential equations of the eighth order with n-deviating arguments. We employ the functional Lyapunov approach and the Krasovskii criteria to prove the main results. The obtained results extend some existing results in the literature.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.55 no.4
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• pp.147-153
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• 2006

In this paper, we propose a new delay-dependent criterion on the robust stability of time-delayed linear systems having norm bounded uncertainties. Based on new form of Lyapunov-Krasovskii functional and the Newton-Leibniz formula, we drive a result in the form of LMI which guarantees the robust stability without any model transformation. The Newton-Leibniz equation was used to relate the cross terms with free matrices. Finally, we show the usefulness of our result by two numerical examples.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.387-397
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• 2017

In order to react the dynamic behavior of the system more actually, it is necessary to solve the first problem of synchronization for Markovian jump complex network system in practical engineering problem. In this paper, the problem of local stochastic synchronization for Markovian nonlinear coupled neural network system is investigated, including nonlinear coupling terms and mode-dependent delays, that is less restriction to other system. By designing the Lyapunov-Krasovskii functional and applying less conservative inequality, we get a new criterion to ensure local synchronization in mean square for Markovian nonlinear coupled neural network system. The criterion introduced some free matrix variables, which are less conservative. The simulation confirmed the validity of the conclusion.

• 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.9
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• pp.1748-1753
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• 2011

In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.4
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• pp.668-676
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• 2008

In this paper, we considered the $H_{\infty}$ tracking control for time-delayed linear systems with saturating actuators. The considered time delay is a time varying one having bounded magnitude and rate, and the considered tracking reference is a general one only known its bounds of magnitude and rate. First, we have converted the $H_{\infty}$ tracking control problem into an equivalent $H_{\infty}$ disturbance attenuation problem using two steps of transformations. Next, based on a new Lyapunov-Krasovskii functional, we have derived the result in the form of LMI with two non-convex parameters. Finally, by numerical examples, we have shown the usefulness and effectiveness of our result.