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Guaranteed interval of delay for a class of non-linear control systems

A new method is proposed in this article in order to determine a guaranteed interval of time delay in input signal for a class of non-linear control systems with state feedback. This method is based on the stability sufficient condition of a non-linear control system using the Lyapunov direct approach. For this purpose, the dynamic equations of the non-linear input-delayed system are reformulated as a non-linear system without delay, but with delay-dependent coefficients in the state-space description. The control strategy is considered a linear state feedback. Then, by introducing an appropriately related Lyapunov candidate, the stability sufficient condition of the closed-loop system is satisfied, leading to a guaranteed interval of delay according to the state feedback gain. The main results are gathered and proved as a lemma. The effectiveness of this proposed method is investigated by simulating the state feedback control of a non-linear synchronous generator with a delay in input.