Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities

This paper addresses the problems of stability and synchronization for a class of Markovian jump neural networks with partly unknown transition probabilities. We first study the stability analysis problem for a single neural network and present a sufficient condition guaranteeing the mean square asymptotic stability. Then based on the Lyapunov functional method and the Kronecker product technique, the chaos synchronization problem of an array of coupled networks is considered. Both the stability and the synchronization conditions are delay-dependent, which are expressed in terms of linear matrix inequalities. The effectiveness of the developed methods is shown by simulation examples.     

Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints

Robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative. This paper overcomes these issues through an augmented autonomous prediction formulation, and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance, namely invariance with probability p.     

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

This paper addresses the stability issue of discrete-time switched systems with guaranteed dwell-time. The approach of switched homogeneous Lyapunov function of higher order is formally proposed. By means of this approach, a necessary and sufficient condition is established to check the exponential stability of the considered system. With the observation that switching signal is actually arbitrary if the dwell time is one sample time, a necessary and sufficient condition is also presented to verify the exponential stability of switched systems under arbitrary switching signals. Using the augmented argument, a necessary and sufficient exponential stability criterion is given for discrete-time switched systems with delays. A numerical example is provided to show the advantages of the theoretical results.     

Strong stability of the mono-tubular heat exchanger equation with output feedback

We investigate asymptotic behavior of the C₀-semigroup T(t) associated with the mono-tubular heat exchanger equation with output feedback by a perturbation method. It is shown that T(t) is bounded if a constraint is satisfied by the parameters and the spatial distribution function. Further, applying the Arendt-Batty-Lyubich-Vu theorem, a criterion is established to judge strong stability of T(t).     

Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems

The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent （r.s.e.） transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality （LMI） conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with 7- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the oaoer.     

Stability analysis in a second-order differential equation with delays

A second-order differential equation with finite discrete delays is considered. Local stability of the zero equilibrium is investigated, and we obtain some sufficient conditions for the zero equilibrium is stable or unstable. Moreover, it is found that there exist the local Hopf bifurcations of the system when the delay varies.     

Oxidation behaviors of Ni-Cr-Al superalloy foams at 1 000 ℃ in air

The oxidation behaviors of Ni-16Cr-xAl （x=4.5%, 9.0%, mass fraction） superalloy foams in air at 1000℃ were investigated. The effects of AI content on the resistance to high temperature oxidation were examined. The oxidation mechanisms of the foams were discussed. The results show that the resistance to the oxidation of the Ni-16Cr-xA1 based alloy at 1 000 ℃ increases with the content of A1 increasing from 4.5% to 9.0%. Complex oxide products are formed on the surface of the superalloy foams after the oxidation. Cr203 and A1203 are the predominant oxides for the scales of the foams with 4.5% A1 and 9% A1, respectively. Excellent high temperature oxidation resistance and superior pore conformation stability for the Ni-16Cr-xA1 based superalloy foam with 9% A1 can be mainly attributed to the formation of relatively continuous and protective A1203 oxides on the surface of the foam.     

Parametric synthesis of pulsar time

A new method of generating pulsar time based on a coherent representation of a sequence of observed events is considered. The properties of pulsar time compared with the traditional approach are analyzed. __________ Translated from Izmeritel’naya Tekhnika, No. 6, pp. 39–44, June, 2006.