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

• Observer-based control of nonlinear systems under input-output delays is studied.
• Time-varying nature of delays is incorporated for the controller design.
• Delay-range-dependent observer-based control is reported.
• Decoupling technique is applied to compute controller and observer gains.
• The control scheme is tested to control a one-link flexible joint robotic arm.

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.