In this brief, a new variable structure proportional-integral-derivative (PID) controller design approach is considered for the tracking stabilization of robot motion. The work corroborates the utility of a certain PID sliding mode controller with PID sliding surface for tracking control of a robotic manipulator. Different from the general approach, the conventional equivalent control term is not used in this controller because that needs to use the matching conditions and exact full robot dynamics knowledge, which involves unavailable parameter uncertainties. Though the sliding surface includes also the integral error term, which makes the robot tracking control problem complicated, the existence of a sliding mode and gain selection guideline are clearly investigated. Moreover, different from uniformly ultimately boundedness, the global asymptotic stability of the robot system with proposed controller is analyzed. The sliding and global stability conditions are formulated in terms of Lyapunov full quadratic form and upper and lower matrix norm inequalities. Reduced design is also discussed. The proposed control algorithm is applied to a two-link direct drive robot arm through simulations. The simulation results indicate that the control performance of the robot system is satisfactory. The chattering phenomenon is handled by the use of a saturation function replaced with a pure signum function in the control law. The saturation function results in a smooth transient performance. The proposed approach is compared with the existing alternative sliding mode controllers for robot manipulators in terms of advantages and control performances. A comparative analysis with a plenty of simulation results soundly confirmed that the performance of developed variable structure PID controller is better under than those of both classical PID controller and an existing variable structure controller with PID-sliding surface.Index Terms-Lyapunov full quadratic form, robot tracking control, sliding mode, variable structure PID controller.

This paper investigates the robust stability for systems with time-varying delay. An improved linear matrix inequality (LMI) based robust delay-dependent stability test is introduced to ensure a larger upper bound for time-varying delays affecting the state vector of an uncertain continuoustime system with norm-bounded type uncertainties. We construct a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation to derive some delay-dependent stability criteria. The proposed method gives sufficient conditions for the robust stability of the system with time-varying delay under norm-bounded uncertainty. Numerical examples indicate that the proposed stability criteria effectively improves the existing results.

In this paper, an improved linear matrix inequality (LMI)-based robust delay-dependent stability test is introduced to ensure a larger upper bound for time-varying delays affecting the state vector of an uncertain continuous-time system with norm-bounded-type uncertainties. A quasi-full-size Lyapunov-Krasovskii functional is chosen and free-weighting matrix approach is employed. Less restrictive sufficient conditions are derived for robust stability of time-varying delay systems with norm-bounded-type uncertainties. Moreover, the investigation of the stabilization problem with memoryless state-feedback control is presented such that the stabilizability criteria are obtained in terms of matrix inequalities, which can be solved via utilizing a cone complementarity minimization algorithm. Finally, the problem of output feedback stabilization for square systems is also taken into consideration. The output feedback stabilizability criteria are derived in the form of linear matrix inequalities, which are convex and can be easily solved using interior point algorithms. A plenty of numerical examples are presented indicating that the proposed stability and stabilization methods effectively improve the existing results. modelling errors or some ignored factors. The subject of uncertain time-delay systems, thus, has received a considerable amount of interest from researchers. See, for example, References [4][5][6][7][8][9][10][11] and the references therein. A number of linear time-invariant control (LTI) system analysis and a framework for a numerical search of quadratic Lyapunov functions are considered in Reference [12]. The stability analysis or stabilization synthesis for time-delay systems can be achieved delay-independently or delay-dependently. Several authors, see, e.g. References [6,8,9], introduce delay-independent results. Since there is no upper limit to time-delay, often delayindependent results can be regarded as conservative in practice where unbounded time delays are not so realistic. Therefore, stability results that depend on the size of the time-delay receive quite a lot of interest. See, for example, some of the delay-dependent results given in References [13][14][15][16][17][18][19][20]. The problems of delay-dependent robust stability analysis and robust control with memoryless state-feedback for a class of uncertain linear systems with time-varying delayed state and norm-bounded uncertainty are considered in Reference [13] based on Razumikhin stability theorem. Robust stabilization and robust H 1 control for uncertain linear constant state-delayed systems is investigated in Reference [14]. Delay-dependent stability conditions are derived in Reference [15] for a class of neutral linear systems in terms of neutral-type model transformation. A non-convex delay-dependent robust stabilization condition is obtained in Reference [16] for uncertain state-delayed systems with a generalized form of inequality to bind the cross-product terms. The delay-dependent robust stability for time-delay systems is inves...

SUMMARYThis paper studies the design problem of robust delay-dependent H ∞ controller for a class of timedelay control systems with time-varying state and input delays, which are assumed to be noncoincident. The system is subject to norm-bounded uncertainties and L 2 disturbances. Based on the selection of an augmented form of Lyapunov-Krasovskii (L-K) functional, first a Bounded Real Lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, unforced time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H ∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H ∞ stabilization criteria are easily extended by employing a well-known bounding technique. A plenty of numerical examples are given to illustrate the application of the proposed methodology of this note. The achieved numerical results on the maximum allowable delay bound and minimum allowable disturbance attenuation level are exhibited to be less conservative in comparison to those of existing methods in the literature.

No abstract