ABSTRACT In this paper, a general class of Halanay-type non-autonomous functional differential in... more ABSTRACT In this paper, a general class of Halanay-type non-autonomous functional differential inequalities is considered. A new concept of stability, namely global generalized exponential stability, is proposed. We first prove some new generalizations of the Halanay inequality. We then derive explicit criteria for global generalized exponential stability of nonlinear non-autonomous time-delay systems based on our new generalized Halanay inequalities. Numerical examples and simulations are provided to illustrate the effectiveness of the obtained results.
ABSTRACT This paper concerns with the problem of exponential stabilization for a class of non-aut... more ABSTRACT This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov–Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.
IMA Journal of Mathematical Control and Information, 2009
Abstract In this paper, we investigate the memory controller design for the exponential stabiliza... more Abstract In this paper, we investigate the memory controller design for the exponential stabilization of linear time-varying systems with control delay. Based on state transformation and an improved LyapunovKrasovskii functional, new sufficient conditions for the ...
... Stability of Time-delay Systems , Boston: Birkhäuser. [CrossRef] View all references; Mondié ... more ... Stability of Time-delay Systems , Boston: Birkhäuser. [CrossRef] View all references; Mondié and Kharitonov 20055. Hien, LV. 2005. ... [Taylor & Francis Online], [Web of Science ®] View all references; Tian and Peng 20066. Hien, LV. 2006. ...
ABSTRACT In this paper, a general class of Halanay-type non-autonomous functional differential in... more ABSTRACT In this paper, a general class of Halanay-type non-autonomous functional differential inequalities is considered. A new concept of stability, namely global generalized exponential stability, is proposed. We first prove some new generalizations of the Halanay inequality. We then derive explicit criteria for global generalized exponential stability of nonlinear non-autonomous time-delay systems based on our new generalized Halanay inequalities. Numerical examples and simulations are provided to illustrate the effectiveness of the obtained results.
ABSTRACT This paper concerns with the problem of exponential stabilization for a class of non-aut... more ABSTRACT This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov–Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.
IMA Journal of Mathematical Control and Information, 2009
Abstract In this paper, we investigate the memory controller design for the exponential stabiliza... more Abstract In this paper, we investigate the memory controller design for the exponential stabilization of linear time-varying systems with control delay. Based on state transformation and an improved LyapunovKrasovskii functional, new sufficient conditions for the ...
... Stability of Time-delay Systems , Boston: Birkhäuser. [CrossRef] View all references; Mondié ... more ... Stability of Time-delay Systems , Boston: Birkhäuser. [CrossRef] View all references; Mondié and Kharitonov 20055. Hien, LV. 2005. ... [Taylor & Francis Online], [Web of Science ®] View all references; Tian and Peng 20066. Hien, LV. 2006. ...
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