Abstract
This paper studies the problem of a guaranteed cost control for a class of stochastic delayed neural networks. The time delay is a continuous function belonging to a given interval, but it is not necessarily differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some mean square exponential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functional, a guaranteed cost controller is designed via memory less state feedback control, and new sufficient conditions for the existence of the guaranteed cost state-feedback for the system are given in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the obtained result.
Highlights
Stability and control of neural networks with the time delay have attracted considerable attention in recent years [ – ]
A guaranteed cost control problem [ – ] has the advantage of providing an upper bound on a given system performance index, and, the system performance degradation, incurred by the uncertainties or time delays, is guaranteed to be less than this bound
To the best of our knowledge, the guaranteed cost control and state feedback stabilization for stochastic neural networks with interval, nondifferentiable time-varying delays have not been fully studied yet, which are important in both theories and applications
Summary
Stability and control of neural networks with the time delay have attracted considerable attention in recent years [ – ]. In the area of control, signal processing, pattern recognition and image processing, and delayed neural networks have many useful applications Some of these applications require that the equilibrium points of the designed network be stable. To the best of our knowledge, the guaranteed cost control and state feedback stabilization for stochastic neural networks with interval, nondifferentiable time-varying delays have not been fully studied yet (see, e.g., [ – ] and the references therein), which are important in both theories and applications.
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