Abstract
The robust stability of uncertain linear neutral systems with time-varying discrete and neutral delays is investigated. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Both delay-dependent and delay-derivative-dependent stability criteria are proposed and are formulated in the form of linear matrix inequalities (LMIs). The results in this paper contain some existing results as their special cases. A numerical example is also given to indicate significant improvements over some existing results.
Highlights
The problem of the stability of delay-differential neutral systems has received considerable attention in the last two decades; for example, [1]
In [15], based on a descriptor model transformation [9] and the decomposition of a discrete delay term matrix, the robust stability of uncertain systems with a single time-varying discrete delay is investigated by applying an integral inequality as compared to the bounding of cross-terms used in [16]
The time-varying vectorvalued functions f ðxðtÞ; tÞ 2 Rn; gðxðt À rðtÞÞ; tÞ 2 Rn and hðx_ðt À tðtÞÞ; tÞ 2 Rn are unknown and represent the parameter perturbations with respect to the current state x(t) and delayed state xðt À rðtÞÞ and x_ðt À tðtÞÞ of the system, respectively. They satisfy that f ð0; tÞ 1⁄4 0; gð0; tÞ 1⁄4 0 and hð0; tÞ 1⁄4 0: The delay r(t) is a time-varying discrete delay and tðtÞ is a time-varying neutral delay, which satisfy: 0 rðtÞ rM r_ðtÞ rd 0 tðtÞ tM t_ðtÞ td ð2Þ
Summary
The problem of the stability of delay-differential neutral systems has received considerable attention in the last two decades; for example, [1]. In [15], based on a descriptor model transformation [9] and the decomposition of a discrete delay term matrix, the robust stability of uncertain systems with a single time-varying discrete delay is investigated by applying an integral inequality as compared to the bounding of cross-terms used in [16]. We will investigate the robust stability of uncertain neutral systems using the Lyapunov-Krasovskii functional approach We will consider both nonlinear parameter perturbations and norm-bounded uncertainties. We will consider the robust stability problem in terms of symmetric positive-definite matrices Both delay-dependent and delay-derivative-dependent stability criteria will be proposed and formulated in the form of linear matrix inequalities (LMIs), which can be effectively solved using interior-point optimisation algorithms [17]. For the case of a constant time-delay, the delay-derivative-dependent criterion reduces to delayindependent one
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
