Delay-dependent stability criteria for LTI systems with multiple time delays

Based on the argument principle, a method is proposed to derive delay-dependent stability criteria without any conservatism for LTI (linear time invariant) systems with multiple time delays. Because the characteristic polynomial of a LTI system with multiple time delays is analytic in the whole complex plane, we use the argument principle to judge whether the characteristic equation has roots in the right-half complex plane. We construct a new function based on the characteristic polynomial so as that the criteria take a straightforward form, and can be used conveniently. The criteria can be considered as a generalized Nyquist criterion. The criteria are sufficient and necessary for the stability of the system. The method involves no symbol calculation so as that can deal easily with the systems of which the orders and time delays are more than 3. The example case study shows that the criteria can judge whether a LTI system is stable exactly, for any given time delays.

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