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Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays
Copyright [2006] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this letter, the global asymptotic stability analysis problem is considered for a class of stochastic Cohen-Grossberg neural networks with mixed time delays, which consist of both the discrete and distributed time delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, a linear matrix inequality (LMI) approach is developed to derive several sufficient conditions guaranteeing the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the addressed stochastic Cohen-Grossberg neural networks with mixed delays are globally asymptotically stable in the mean square if two LMIs are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also pointed out that the main results comprise some existing results as special cases. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria
Stabilisation of hybrid stochastic differential equations by delay feedback control
This paper is concerned with the exponential mean-square stabilisation of hybrid stochastic differential equations (also known as stochastic dierential equations with Markovian switching) by delay feedback controls. Although the stabilisation by non-delay feedback controls for such equations has been discussed by several authors, there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap. To make our theory more understandable as well as to avoid complicated notations, we will restrict our underlying hybrid stochastic dierential equations to a relatively simple form. However our theory can certainly be developed to cope with much more general equations without any diculty
Minimal data rate stabilization of nonlinear systems over networks with large delays
Control systems over networks with a finite data rate can be conveniently
modeled as hybrid (impulsive) systems. For the class of nonlinear systems in
feedfoward form, we design a hybrid controller which guarantees stability, in
spite of the measurement noise due to the quantization, and of an arbitrarily
large delay which affects the communication channel. The rate at which feedback
packets are transmitted from the sensors to the actuators is shown to be
arbitrarily close to the infimal one.Comment: 16 pages; references have now been adde
Time and frequency domain analysis of sampled data controllers via mixed operation equations
Specification of the mathematical equations required to define the dynamic response of a linear continuous plant, subject to sampled data control, is complicated by the fact that the digital components of the control system cannot be modeled via linear ordinary differential equations. This complication can be overcome by introducing two new mathematical operations; namely, the operation of zero order hold and digial delay. It is shown that by direct utilization of these operations, a set of linear mixed operation equations can be written and used to define the dynamic response characteristics of the controlled system. It also is shown how these linear mixed operation equations lead, in an automatable manner, directly to a set of finite difference equations which are in a format compatible with follow on time and frequency domain analysis methods
Integral Input-to-State Stability of Nonlinear Time-Delay Systems with Delay-Dependent Impulse Effects
This paper studies integral input-to-state stability (iISS) of nonlinear
impulsive systems with time-delay in both the continuous dynamics and the
impulses. Several iISS results are established by using the method of
Lyapunov-Krasovskii functionals. For impulsive systems with iISS continuous
dynamics and destabilizing impulses, we derive two iISS criteria that guarantee
the uniform iISS of the whole system provided that the time period between two
successive impulse moments is appropriately bounded from below. Then we provide
an iISS result for systems with unstable continuous dynamics and stabilizing
impulses. For this scenario, it is shown that the iISS properties are
guaranteed if the impulses occur frequently enough. For impulsive systems with
stabilizing impulses and stable continuous dynamics for zero input, we obtain
an iISS result which shows that the entire system is uniformly iISS over
arbitrary impulse time sequences. As applications, iISS properties of a class
of bilinear systems are studied in details with simulations to demonstrate the
presented results
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