• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.57-69
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• 2012

In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.

• International Journal of Control, Automation, and Systems
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• v.3 no.4
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• pp.524-532
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• 2005

This paper concerns delay-dependent guaranteed cost control (GCC) problem for a class of linear state-delayed systems with norm-bounded time-varying parametric uncertainties. By incorporating the free weighing matrix approach developed recently, new delay-dependent conditions for the existence of the guaranteed cost controller are presented in terms of matrix inequalities for both nominal state-delayed systems and uncertain state-delayed systems. An algorithm involving convex optimization is proposed to design a controller achieving a suboptimal guaranteed cost such that the system can be stabilized for all admissible uncertainties. Through numerical examples, it is shown that the proposed method can yield less guaranteed cost than the existing delay-dependent methods.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.05a
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• pp.469-470
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• 2010

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.1
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• pp.193-198
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• 2009

In this paper, we consider the design problem of delay-dependent robust $H{\infty}$ controller of discrete-time descriptor systems with parameter uncertainties and interval time-varying delays in state and control input by delay-dependent LMI (linear matrix inequality) technique. A new delay-dependent bounded real lemma for discrete-time descriptor systems with time-varying delays is derived. The condition for the existence of robust $H{\infty}$ controller and the robust $H{\infty}$ state feedback control law are proposed by LMI approach. A numerical example is demonstrated to show the validity of the design method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.1
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• pp.51-82
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• 2016

In view of ideas for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is generally included with existence and controllability (EaC) results for fractional neutral integro-differential systems (FNIDS) with state-dependent delay (SDD) in Banach spaces. Finally, an examples are also provided to illustrate the theoretical results.

• International Journal of Control, Automation, and Systems
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• v.6 no.4
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• pp.515-525
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• 2008

In this paper, the problem of delay-dependent stabilization for singular systems with multiple internal and external incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily test with numerical or algebraic methods. Based on Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memoryless state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free, and asymptotically stable via solving a strict linear matrix inequality (LMI) problem. An explicit expression for the desired memoryless state feedback control laws is also given. Finally, a numerical example illustrates the effectiveness and the availability for the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1744-1746
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• 2004

This paper focuses on the problem of asymptotic stabilization for time-delay systems. To this end, a memoryless state feedback controller is proposed. Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between the terms in the Leibniz-Newton formula into account. Certain free weighting matrices are used to express this relationship and linear matrix inequalities (LMIs)-based algorithm to design the controller stabilizing the system.

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.2
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• pp.121-127
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• 2009

This paper deals with the design problem of robust stabilization and non-fragile controller for discrete-time singular systems with parameter uncertainties and time-varying delays in state and input by delay-dependent Linear Matrix Inequality (LMI) approach. A new delay-dependent bounded real lemma for singular systems with time-varying delays is derived. Robust stabilization and robust non-fragile state feedback control laws are proposed, which guarantees that the resultant closed-loop system is regular, causal and stable in spite of time-varying delays, parameter uncertainties, and controller gain variations. A numerical example is given to show the validity of the design method.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.151-184
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• 2022

In the article, we handle with the existence and controllability results for fractional impulsive neutral functional integro-differential equation in Banach spaces. We have used advanced phase space definition for infinite delay. State dependent infinite delay is the main motivation using advanced version of phase space. The results are acquired using Schaefer's fixed point theorem. Examples are given to illustrate the theory.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1271-1290
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• 2011

The purpose of this paper is to investigate the controllability of certain types of second order nonlinear impulsive systems with statedependent delay. Sufficient conditions are formulated and the results are established by using a fixed point approach and the cosine function theory Finally examples are presented to illustrate the theory.