Finite-Time Boundedness of Markov Jump System with Piecewise-Constant Transition Probabilities via Dynamic Output Feedback Control

This paper first investigates the problem of finite-time boundedness of Markovian jump system with piecewise-constant transition probabilities via dynamic output feedback control, which leads to both stochastic jumps and deterministic switches. Based on stochastic Lyapunov functional, the concept of finite-time boundedness, average dwell time, and the coupling relationship among time delays, several sufficient conditions are established for finite-time boundedness and H∞ filtering finite-time boundedness. The system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method

Further analysis of stability of uncertain neural networks with multiple time delays

This paper studies the robust stability of uncertain neural networks with multiple time delays with respect to the class of nondecreasing activation functions. By using the Lyapunov functional and homeomorphism mapping theorems, we derive a new delay-independent sufficient condition the existence, uniqueness, and global asymptotic stability of the equilibrium point for delayed neural networks with uncertain network parameters. The condition obtained for the robust stability establishes a matrix-norm relationship between the network parameters of the neural system, and therefore it can easily be verified. We also present some constructive numerical examples to compare the proposed result with results in the previously published corresponding literature. These comparative examples show that our new condition can be considered as an alternative result to the previous corresponding literature results as it defines a new set of network parameters ensuring the robust stability of delayed neural networks.Publisher's Versio

Stability Analysis of Stochastic Markovian Jump Neural Networks with Different Time Scales and Randomly Occurred Nonlinearities Based on Delay-Partitioning Projection Approach

In this paper, the mean square asymptotic stability of stochastic Markovian jump neural networks with different time scales and randomly occurred nonlinearities is investigated. In terms of linear matrix inequality (LMI) approach and delay-partitioning projection technique, delay-dependent stability criteria are derived for the considered neural networks for cases with or without the information of the delay rates via new Lyapunov-Krasovskii functionals. We also obtain that the thinner the delay is partitioned, the more obviously the conservatism can be reduced. An example with simulation results is given to show the effectiveness of the proposed approach

Robust Exponential Stabilization of Stochastic Delay Interval Recurrent Neural Networks with Distributed Parameters and Markovian Jumping by Using Periodically Intermittent Control

We consider a class of stochastic delay recurrent neural networks with distributed parameters and Markovian jumping. It is assumed that the coefficients in these neural networks belong to the interval matrices. Several sufficient conditions ensuring robust exponential stabilization are derived by using periodically intermittent control and Lyapunov functional. The obtained results are very easy to verify and implement, and improve the existing results. Finally, an example with numerical simulations is given to illustrate the presented criteria

Spectral Perspective on the Stability of Discrete-Time Markov Jump Systems with Multiplicative Noise

We apply the spectrum analysis approach to address the stability of discrete-time Markov jump systems with state-multiplicative noise. In terms of the spectral distribution of a generalized Lyapunov operator, spectral criteria are presented to testify three different kinds of stochastic stabilities: asymptotic mean square stability, critical stability, and essential instability

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this paper, the problem of stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen–Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.This work was supported by the Natural Science Foundation of CQ CSTC under grant 2007BB0430, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant KJ070401, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Dissipative Analysis and Synthesis of Control for TS Fuzzy Markovian Jump Neutral Systems

This paper is focused on stochastic stability and strictly dissipative control design for a class of Takagi-Sugeno (TS) fuzzy neutral time delayed control systems with Markovian jumps. The main aim of this paper is to design a strictly dissipative controller such that the closed-loop TS fuzzy control system is stochastically stable, and also the disturbance rejection attenuation is obtained to a given level by means of the H∞ performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of desired dissipative controller which ensures both the stochastic stability and the strictly dissipative performance. The main advantage of the proposed technique is that it is possible to obtain the dissipative controller with less control effort and also, as special cases, robust H∞ control with the prescribed H∞ performance under given constraints and passivity control can be obtained for the considered systems. Also, the existence condition of the fuzzy dissipative controller can be obtained in terms of linear matrix inequalities. Finally, a practical example based on truck-trailer model is provided to demonstrate the effectiveness and feasibility of the proposed design technique