Stability analysis of Lur'e indirect control systems with time delay and multiple nonlinearities

In this paper, Lur'e indirect control systems with sector-type nonlinearities and a constant delay in the feedback law are studied. With the aid of an original construction of complete-type Lyapunov-Krasovskii functional, new conditions of the delay-independent asymptotic stability for the zero solutions of the considered systems are obtained. Furthermore, estimates for convergence rate of solutions are derived and stability robustness is analyzed. Finally, using a modification of the averaging approach, conditions are found under which time-varying perturbations with zero mean values do not disturb the stability of the zero solutions. Results of numerical simulations are presented confirming the theoretical conclusions.