• Title, Summary, Keyword: state-dependent delay

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SOLVABILITY OF IMPULSIVE NEUTRAL FUNCTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS WITH STATE DEPENDENT DELAY

  • Karthikeyan, K.;Anguraj, A.
    • 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.

Delay-dependent Guaranteed Cost Control for Uncertain State-delayed Systems

  • Lee Young Sam;Kwon Oh-Kyu;Kwon Wook Hyun
    • 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.

Delay-dependent Robust $H_{\infty}$ Control for Uncertain Discrete-time Descriptor Systems with Interval Time-varying Delays in State and Control Input (상태와 입력에 구간 시변 시간지연을 가지는 불확실 이산시간 특이시스템의 지연 종속 강인 $H_{\infty}$ 제어)

  • Kim, Jong-Hae
    • 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.

EXISTENCE AND CONTROLLABILITY OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL SYSTEMS WITH STATE-DEPENDENT DELAY IN BANACH SPACES

  • KAILASAVALLI, SUBRAMANIAN;SUGANYA, SELVARAJ;ARJUNAN, MANI MALLIKA
    • 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.

Delay-dependent Stabilization of Singular Systems with Multiple Internal and External Incommensurate Constant Point Delays

  • Xie, Yong-Fang;Gui, Wei-Hua;Jiang, Zhao-Hui
    • 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.

Delay-dependent stabilization for time-delay systems;An LMI approach

  • Cho, H.J.;Park, Ju-H.;Lee, S.G.
    • 제어로봇시스템학회:학술대회논문집
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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.

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Delay-Dependent Robust Stabilization and Non-Fragile Control of Uncertain Discrete-Time Singular Systems with State and Input Time-Varying Delays (상태와 입력에 시변 시간지연을 가지는 불확실 이산시간 특이시스템의 지연종속 강인 안정화 및 비약성 제어)

  • Kim, Jong-Hae
    • 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.

CONTROLLABILITY OF SECOND-ORDER IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

  • Arthi, Ganesan;Balachandran, Krishnan
    • 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.

A Delay-Dependent Approach to Robust Filtering for LPV Systems with Discrete and Distributed Delays using PPDQ Functions

  • Karimi Hamid Reza;Lohmann Boris;Buskens Christof
    • International Journal of Control, Automation, and Systems
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    • v.5 no.2
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    • pp.170-183
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    • 2007
  • This paper presents a delay-dependent approach to robust filtering for linear parameter-varying (LPV) systems with discrete and distributed time-invariant delays in the states and outputs. It is assumed that the state-space matrices affinely depend on parameters that are measurable in real-time. Some new parameter-dependent delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs) such that the filtering process remains asymptotically stable and satisfies a prescribed $H_{\infty}$ performance level. Using polynomially parameter-dependent quadratic (PPDQ) functions and some Lagrange multiplier matrices, we establish the parameter-independent delay-dependent conditions with high precision under which the desired robust $H_{\infty}$ filters exist and derive the explicit expression of these filters. A numerical example is provided to demonstrate the validity of the proposed design approach.