M. N. Alpaslan Parlakci

Robust delay-dependent guaranteed cost controller design for uncertain neutral systems

In this paper, a novel robust delay-dependent guaranteed cost controller is introduced for a class of uncertain nonlinear neutral systems with both norm-bounded uncertainties and nonlinear parameter perturbations. A neutral memory state-feedback control law is chosen such that a quadratic cost function is minimized. On the basis of a descriptor type model transformation, an augmented descriptor form Lyapunov-Krasovskii functional is proposed in order to derive a linear matrix inequality (LMI) condition of the synthesis of a robust stabilizing guaranteed cost controller for uncertain nonlinear neutral systems. The descriptor approach is applied for both the delay-differential equation and the neutral difference operator allowing to introduce several additional free weighting matrices in order to obtain further relaxation in the synthesis process. The proposed method of introducing some relaxation into design problem also leads to develop LMI conditions which can be easily solved using interior point algorithms. Two numerical examples have been introduced to show the application of the theoretical results which indicate that the proposed approach improves the guaranteed cost performance.

A NEW VARIABLE STRUCTURE PID-CONTROLLER FOR ROBOT MANIPULATORS WITH PARAMETER PERTURBATIONS: AN AUGMENTED SLIDING SURFACE APPROACH

Abstract 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 LMIs techniques and principle of Rayleighs 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.

Stability of Interval Time-Varying Delay Systems: A Nonuniform Delay Partitioning Approach

Abstract 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.

Further Stability Criteria for Time-Delay Systems with Interval Time-Varying Delays

Abstract 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.

ℒ 2 - gain control of time-delay systems with actuator saturation

Disturbance attenuation problem in terms of ℒ2-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.

Stability of retarded time-delay systems: Extensively augmented lyapunov functional approach

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.

H∞ OUTPUT FEEDBACK CONTROL FOR UNCERTAIN NEUTRAL TIME-DELAY SYSTEMS:AUGMENTED DYNAMICS AND AUGMENTED LYAPUNOV FUNCTIONAL APPROACHES

Abstract In this paper the robust H∞ output feedback control of uncertain neutral time-delay systems with norm-bounded type uncertainties is investigated. The control input is utilized as the augmenting state term and the system is represented in augmented dynamics form which enables to handle the design of the H∞ output feedback controller in terms of convex linear matrix inequalities (LMI) form which can be solved via interior-point algorithms. A novel augmented Lyapunov-Krasovskii functional is selected to obtain sufficient LMI conditions for the existence of delay-dependent H∞ output feedback control. Any model transformation and bounding for cross terms are strictly avoided to overcome the conservativeness of the results. A delay-dependent bounded real lemma is also presented in LMI form. Finally, several numerical examples are given to illustrate the effectiveness of the proposed method.

DELAY-DEPENDENT ROBUST STABILITY OF UNCERTAIN NEUTRAL SYSTEMS: QUASI FULL SIZE LYAPUNOV FUNCTIONAL APPROACH

Abstract In this paper a new class of augmented quasi full size Lypunov-Krasovskii functional is introduced for the robust stability of linear uncertain neutral systems. The nonlinear parameter perturbations and norm bounded uncertainties are taken into consideration separately. Delay-dependent robust stability criteria are derived in the form of linear matrix inequalities. Numerical examples are presented to illustrate the significant improvement on the conservativeness of the delay bound over some reported results in the literature.