Delay-range-dependent observer-based control of nonlinear systems under input and output time-delays

Raafia Majeed, Sohaira Ahmad and Muhammad Rehan

Applied Mathematics and Computation, 2015, vol. 262, issue C, 145-159

Abstract: The problem of designing observer-based controller for a class of nonlinear time-delay systems subjected to input and output time-varying delays is addressed in this paper. More incisively, a delay-range-dependent criterion, incorporating variation of delays between known lower and upper bounds, is established for control of nonlinear time-delay systems. The proposed methodology ensures asymptotic stability of the closed-loop system's state and the estimation error between states of the system and observer. By application of a Lyapunov–Krasovskii functional, Jensen's inequality, standard matrix inequality procedures, Luenberger-type observer, delay-interval bounds and delay-derivative limits, observer-based controller synthesis approach using nonlinear matrix inequalities for the nonlinear time-delay systems is provided. Further, a decoupling approach is employed to render a simpler condition for the observer and the controller synthesis. A novel observer-based control scheme for the linear time-delay systems with interval time-varying input as well as output lags is derived from the proposed control strategy. The traditional delay-dependent controller design, incorporating zero lower bound of the delay, for the time-delay systems is a particular scenario of the projected delay-range-dependent approach. The proposed decoupled observer-based controller synthesis condition is cast into linear matrix inequalities by means of the cone complementary linearization approach. Finally, a numerical simulation example of control of one-link flexible joint robotic arm is provided to verify the proposed design methodology.

Keywords: Observer-based control; Decoupling technique; Nonlinear time-delay systems; Delay-range-dependency; Input and output delays (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:262:y:2015:i:c:p:145-159

DOI: 10.1016/j.amc.2015.04.052

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