Abstract
In this paper, the μ-stability analysis issue of nonlinear differential systems along with two kinds of delay components, namely, leakage delay and transmission delay, is investigated. By constructing a suitable Lyapunov–Krasovskii's functional and utilizing Finsler's lemma, some novel μ-stability criteria for the concerned nonlinear system are obtained. These criteria are expressed in the framework of linear matrix inequalities (LMIs), which can be verified easily by means of standard software. Finally, two examples are presented to exhibit the advantage and effectiveness of the proposed theoretical results.
Highlights
Introduction or the first sectionIt is obvious that time delay often occur in many industrial and engineering systems, such as chemical engineering systems, long transmission lines in pneumatic systems, population dynamic models, network control systems, etc
By applying the Finsler’s Lemma and constructing appropriate Lyapunov–Krasovskii functional, several delay-dependent μ-stability conditions of the addressed system are derived in the form of linear matrix inequalities (LMIs)
In this paper, we have examined the μ-stability of nonlinear differential systems with bounded and unbounded additive time-varying leakage delays
Summary
It is obvious that time delay often occur in many industrial and engineering systems, such as chemical engineering systems, long transmission lines in pneumatic systems, population dynamic models, network control systems, etc. It is worth pointing out that information on the additive delays is not suitably taken into account in the aforementioned works, and the introduction of many slack variables inevitably increases the computational burden, which motivates the study of this paper Inspired by this idea, in this paper, μ-stability of nonlinear differential. By applying the Finsler’s Lemma and constructing appropriate Lyapunov–Krasovskii functional, several delay-dependent μ-stability conditions of the addressed system are derived in the form of linear matrix inequalities (LMIs). These conditions can be tested with any of the available numerical packages. The notation ∗ denotes the symmetric terms in a symmetric matrix
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