The stabilization problem is investigated for a class of uncertain systems with multiple time-varying delays. The considered system includes the uncertain nonlinear time delay functions, whose bounds are in the form of polynomial-type functions with unknown coefficients. The system is decomposed into two subsystems based on the input matrix. For the first subsystem, a time delay dependent linear virtual control input is constructed. Then, a memoryless state feedback controller is designed based on backstepping method. By employing new Lyapunov–Krasovskii functional, we show that the closed-loop system is exponentially stable. Finally, simulations are conducted to verify the effectiveness of the proposed method.
Memoryless Adaptive Controller Design for Uncertain Polynomial Systems With Multiple Time Delays
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Hua, C., Wang, Q., Shi, P., and Guan, X. (June 9, 2008). "Memoryless Adaptive Controller Design for Uncertain Polynomial Systems With Multiple Time Delays." ASME. J. Dyn. Sys., Meas., Control. July 2008; 130(4): 044504. https://doi.org/10.1115/1.2936867
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