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Öğe ?2 - Gain control of time-delay systems with actuator saturation(2010) Parlakçi, M.N.A.; Küçükdemiral, I.B.Disturbance attenuation problem in terms of ?2-gain for continuous linear time-delay (LTD) systems with nonzero initial conditions, time-varying delays and saturating control is addressed where the disturbances acting on the system are with bounded energy. First, a group of sufficient conditions in terms of bilinear matrix inequalities (BMIs) are obtained. Then, to solve this problem, cone complementary linearization method is adopted to the problem. The proposed method utilizes convex description of nonlinear saturation phenomenon by means of convex hull of some linear feedback which leads to a few additional ellipsoidal conditions in terms of linear matrix inequalities (LMIs). The validity of the method is illustrated through some examples at the end. © 2010 IEEE.Öğe A new robust continuous sliding mode control for robot manipulators with parameter perturbations(2002) Istefanopulos, Y.; Jafarov, E.M.; Parlakçi, M.N.A.In this paper a new continuous sliding mode controller is designed for stabilization of robot manipulator systems with parameter perturbations. The sufficient conditions for the existence of a sliding mode in the robot system is considered. The techniques of matrix norm inequalities are used to cope with robustness issues. Some effective parameter-independent conditions are developed in a concise manner for the globally asymptotic stability of the multivariable system using linear matrix inequalities (LMI) and principle of Rayleigh's min/max matrix eigenvalue inequality. The stability conditions are derived by using the Lyapunov full quadratic form. The parameter perturbations of the robot motion are evaluated by the Frobenius norm. Simulation results have shown that the control performance of the robot system is satisfactory.Öğe A new variable structure PID-controller for robot manipulators with parameter perturbations: An augmented sliding surface approach(IFAC Secretariat, 2002) Jafarov, E.M.; Istefanopulos, Y.; Parlakçi, M.N.A.In this paper a new variable structure PID-controller is designed for stabilization of robot manipulator systems with parameter perturbations. The sufficient conditions for the existence of a sliding mode is considered. The techniques of matrix norm inequalities are used to cope with robustness issues. Some effective parameter-independent conditions are developed in a concise manner for the global asymptotic stability of the multivariable system using LMI's techniques and principle of Rayleigh's min/max matrix eigenvalue inequality. The stability conditions are derived by using the Lyapunov full quadratic form for the first time. The parameter perturbations of the robot motion are evaluated by introducing Frobenius norm. Simulation results have shown that the control performance of the robot system is satisfactory. Copyright © 2002 IFAC.Öğe An improved augmented delay partitioning approach for the stability of time-varying state-delayed systems(IFAC Secretariat, 2012) Parlakçi, M.N.A.; Küçükdemiral, I.B.This paper deals with the asymptotical stability problem of retarded type time-delay systems with time-varying delays using the technique of decomposing the delay interval uniformly into an integer number of equal size segments and proposing an appropriate Lyapunov-Krasovskii (L-K) functional to develop delay-dependent stability criteria. The novelty of the proposed method originates from two significant contributions. First, a quasi-full size augmented form of L-K functional is introduced for the stability analysis. Second, almost exact full information has been exploited for the relationship among the actual time-varying delay and its upper bound concerning the delay related integral terms. This approach allows to avoid any redundant enlargement with the delay upper bound while estimating the derivative of the L-K functional as it will bring naturally conservativeness on the results. Several numerical examples are taken into account with some case studies to illustrate the effectiveness of the proposed method. For the treated examples, the results of maximum admissible delay bound have clearly indicated that the proposed approach provides significant improvement over those reported in the literature. © 2012 IFAC.Öğe An lmi approach to static output feedback stabilization for linear continuous-time systems with parameter perturbations(2009) Parlakçi, M.N.A.This paper investigates the design of a robust static output feedback controller for a class of linear continuous-time systems with norm-bounded time-varying parameter perturbations. A descriptor type model transformation and the utilization of free weighting matrices approach are taken into consideration. A linear matrix inequality approach is proposed to develop some sufficient conditions for the existence of a static output feedback controller. Numerical examples are used to demonstrate the effectiveness and applicability of the proposed methodology. Copyright © 2009 Watam Press.Öğe Design of robust PD-sliding mode controller for robot position systems with parameter perturbations(IFAC Secretariat, 2003) Parlakçi, M.N.A.; Jafarov, E.M.; Istefanopulos, Y.This paper introduces a new robust position variable structure controller design method for robot position systems with parameter perturbations. In most situations, the exact knowledge of the robot dynamics does not exist. For this reason a robust variable structure PD-conirol scheme is proposed for the set-point regulation problem of robot systems. The controller compensates the inexact information about the robot system. It uses only some robot bound parameters and measurable joint variables. The sufficient conditions are derived for the existence of a sliding mode in the robot system. The techniques of matrix norm inequalities are often addressed for robustness analysis of the controller. In addition, the stability conditions are also investigated in a global sense. Effective parameter-independent conditions are developed by using a full quadratic form of Lyapunov function. Simulation results have been presented indicating thai the control performance is satisfactory. Copyright © 2003 IFAC.Öğe Further stability criteria for time-delay systems with interval time-varying delays(IFAC Secretariat, 2011) Parlakçi, M.N.A.; Küçükdemiral, I.B.In this paper, a novel stability criterion is developed for time-delay systems having time-varying delays that belong to a given range. Based on a choice of different type of Lyapunov -Krasovskii functional in an extensively augmented form, some new delay-range dependent stability criteria are proposed. This developed stability result has advantages over some previous ones. First, the method is based on the selection of a new, extensively augmented Lyapunov-Krasovskii functional which does not only take the delay range into account but also the weighted version of it. Second it estimates the upper bound of the derivative of the Lyapunov functional without ignoring some useful integral terms. Finally, we have introduced several free slack variables in relation with Newton-Leibniz formula to provide some kind of relaxation for the proposed stability criteria. In addition to this, we have also employed the method of completing to squares which has enabled to provide further relaxation with some additional decision variables. © 2011 IFAC.Öğe Robust delay-dependent stabilizing control of time-delay systems with state and input delays: Augmented L.K. functional approach(IFAC Secretariat, 2010) Parlakçi, M.N.A.; Küçükdemiral, I.B.In this paper, we investigate the design problem of a stabilizing control for a class of linear uncertain time-delay systems with time-varying state and input delays. The control law is selected to be a state-feedback controller. Adopting to employ an augmented type of Lyapunov-Krasovskii functional, for the nominal case, we first derive some sufficient delay dependent stabilization criteria which can be solved using a convex optimization technique with interior-point algorithms. The stabilization synthesis is then extended to the case when the time-delay system is subject to the norm-bounded uncertainties which affect state and input matrices. Several numerical examples are presented to demonstrate the application of the proposed synthesis of a stabilizing controller. The numerical results on the maximum allowable delay bound and the uncertainty bound seem to be quite less conservative in comparison to the existing methods from the literature.Öğe Robust delay-free observer-based controller design for uncertain neutral time delay systems(2006) Parlakçi, M.N.A.This paper deals with the problem of designing robust delay-free observer-based controller for a class of neutral time delay systems with parameter uncertainties. A new linear matrix inequality approach is developed for designing the robust delay-free state-feedback controller that can simultaneously guarantee the global asymptotical stability of the estimation process and closed-loop system independently of the time delay. Employing Lyapunov stability method and quadratic stability theory, new delay-independent stability criteria are obtained in the form of linear matrix inequalities which can be easily solved by well-known interior-point algorithms. Two numerical examples are introduced to demonstrate the effectiveness of the proposed method through simulation studies.Öğe Robust stability and robust stabilization of uncertain linear time-delay systems [2-s2.0-11144291648](2004) Parlakçi, M.N.A.In this paper, the problem of robust stability analysis and robust stabilization with memoryless state feedback control for linear systems with time-varying delayed state and norm-bounded time-varying uncertainties are investigated. The proposed method employs Leibniz-Newton type model transformation, but unlike existing approaches, it does not involve any additional dynamics. As the additional dynamics induce additional eigenvalues that may move into the right-hand complex s-plane before any of the eigenvalues of the original system does, it causes conservatism in the system. Moreover, quite a few existing methods do apply Leibniz-Newton model transformation without including additional dynamics. However, the matrix inequalities that they obtained are not in the form of linear matrix inequalities. Thus, these matrix inequalities could not be solved by using any convex optimization algorithms. Instead, they could only give suboptimal maximal delay bounds. However, our proposed stability and stabilization criteria depending on both the size of the time delay and its derivative are derived in the form of solvable linear matrix inequalities that can be easily converted into a generalized eigenvalue minimization problem. Numerical examples given for the purpose of comparison with some existing results show that the proposed robust stability and robust stabilization criteria yield less conservative results.Öğe Robust stability and robust stabilization of uncertain linear time-delay systems [2-s2.0-33645061777](2005) Parlakçi, M.N.A.In this paper, the problem of robust stability analysis and robust stabilization with memoryless state feedback control for linear systems with time-varying delayed state and norm-bounded timevarying uncertainties are investigated. The proposed method employs Leibnitz-Newton type model transformation, but unlike existing approaches, it does not involve any additional dynamics. As the additional dynamics induce additional eigenvalues that may move into the right-hand complex s-plane before any of the eigenvalues of the original system does, it causes conservatism in the system. Moreover, quite a few existing methods do apply Leibnitz-Newton model transformation without including additional dynamics. However, the matrix inequalities that they obtained are not in the form of linear matrix inequalities. Thus, these matrix inequalities could not be solved by using any convex optimization algorithms. Instead, they could only give suboptimal maximal delay bounds. However, our proposed stability and stabilization criteria depending on both the size of the time delay and its derivative are derived in the form of solvable linear matrix inequalities that can be easily converted into a generalized eigenvalue minimization problem. Numerical examples given for the purpose of comparison with some existing results show that the proposed robust stability and robust stabilization criteria yield less conservative results.Öğe Robust stability of linear systems with delayed perturbations(2004) Parlakçi, M.N.A.In this paper, a new sufficient delay independent robust stability condition is introduced for a class of linear systems with unstructured time-varying delayed perturbations. The stability condition is formulated in terms of the solution of a Lyapunov equation. Since this method needs the tuning of a positive definite symmetric matrix for which there is no any tuning procedure, the stability condition is also given in a solvable linear matrix inequalities (LMI) form. The LMI formulation does not require the tuning of any parameter. The result based on the solution of a Lyapunov equation is analytically shown that the robust stability bound is invariant when a system and its dual system with constant delay time are considered. A numerical example is given for the computation of the robust stability bound. A brief comparison with the previously reported results is also presented.Öğe Robust stability of time delay systems with nonlinear perturbations(2004) Parlakçi, M.N.A.In this paper the robust stability of a class of delayed systems with nonlinear time-varying parameter perturbations is investigated. Based on the Lyapunov stability method and quadratic stability theory, some novel delay-dependent robust stability criteria are derived. Unlike some existing methods, the main distinguishing feature of the proposed method is that any bounding of the cross-terms are not used in the stability analysis. This allows the newly obtained stability criteria to provide less conservative results than that of reported methods which often employ strict bounding for the cross-terms. As the stability criteria are given in the form of linear matrix inequalities, they can be easily solved by using interior-point algorithms. This indicates that the proposed method does not require tuning of any parameters and/or matrices for which it is rather difficult to give an optimization algorithm. Several numerical examples are considered for the purpose of comparison with some previously reported stability results from the literature in order to illustrate the effectiveness of the proposed method.Öğe Stability of interval time-varying delay systems: A nonuniform delay partitioning approach(IFAC Secretariat, 2009) Parlakçi, M.N.A.This paper investigates the conservatism reduction of Lyapunov-Krasovskii based conditions for the stability of a class of interval time-varying delay systems. The main idea is based on the nonuniform decomposition of the integral terms of the Lyapunov-Krasovskii functional. The delay interval is decomposed into a finite number of nonuniform segments with some scaling parameters. Both differentiable delay case and nondifferentiable delay case or unknown delay derivative bound case are taken into consideration. Sufficient delay-dependent stability criteria are derived in terms of matrix inequalities. Introducing a cone complementary problem, a convex optimization algorithm is obtained so that a suboptimal maximum allowable delay upper bound is achieved. Two numerical examples with case studies are given to demonstrate the effectiveness of the proposed method with respect to some existing ones from the literature. Copyright © IFAC 2009.Öğe Stability of retarded time-delay systems: Extensively augmented Lyapunov functional approach(2007) Parlakçi, M.N.A.The problem of stability of linear time-delay systems of retarded type is taken into consideration. A new extensively augmented Lyapunov-Krasovskii functional is introduced and some sufficient delay-dependent stability criteria are derived in terms of linear matrix inequalities (LMIs). Utilization of any model transformation method or any kind of bounding for the cross terms are strictly avoided in the stability analysis. Moreover, in order to reduce the complexity of the solution of the LMI set, the proposed method does not also employ any relaxation such as the recently given free weighting matrix approach. A numerical example is illustrated to indicate the effectiveness of the proposed method. © ICROS.
