scholarly journals Input-to-State Stability of Lur’e Hyperbolic Distributed Complex-Valued Parameter Control Systems: LOI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Zhixin Tai ◽  
Xingcheng Wang ◽  
Yan Shi ◽  
Hamid Reza Karimi
Keyword(s):  
Linear Operator ◽  
Control Systems ◽  
Comparison Principle ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Parameter Control ◽  
Operator Inequalities ◽  
Work Input ◽  
Delay Dependent ◽  
Complex Valued

In this work, input-to-state stability of Lur’e hyperbolic distributedcomplex-valuedparameter control systems has been addressed. Using comparison principle, delay-dependent sufficient conditions for the input-to-state stability in complex Hilbert spaces are established in terms of linear operator inequalities. Finally, numerical computation illustrates our result.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

REFINEMENTS OF THE CONTINUOUS TRIANGLE INEQUALITY FOR THE BOCHNER INTEGRAL IN HILBERT SPACES

2008 ◽  
Vol 01 (04) ◽  
pp. 521-533
Author(s):  
S. S. Dragomir
Keyword(s):  
Hilbert Spaces ◽  
Triangle Inequality ◽  
Bochner Integral ◽  
Numerical Radius ◽  
Operator Inequalities ◽  
Vector Valued Functions ◽  
Complex Valued ◽  
Vector Valued

Some refinements of the continuous triangle inequality for the Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for norm and numerical radius operator inequalities are provided. A particular case of interest for complex-valued functions is pointed out as well.

scholarly journals New Type of Sturm-Liouville Problems in Associated Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
O. Sh. Mukhtarov ◽  
K. Aydemir
Keyword(s):  
Linear Operator ◽  
Asymptotic Behaviour ◽  
Spectral Parameter ◽  
Hilbert Spaces ◽  
Resolvent Operator ◽  
Sufficient Conditions ◽  
Transmission Conditions ◽  
Continuous Case ◽  
New Type ◽  
Sturm Liouville

We introduce a new type of discontinuous Sturm-Liouville problems, involving an abstract linear operator in equation. By suggesting own approaches we define some new Hilbert spaces to establish such properties as isomorphism, coerciveness, and maximal decreasing of resolvent operator with respect to spectral parameter. Then we find sufficient conditions for discreteness of the spectrum and examine asymptotic behaviour of eigenvalues. Obtained results are new even for continuous case, that is, without transmission conditions.

scholarly journals Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Chun-xia Dou ◽  
Zhi-sheng Duan ◽  
Xing-bei Jia ◽  
Xiao-gang Li ◽  
Jin-zhao Yang ◽  
...  
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Upper Bound ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Large System ◽  
Disturbance Attenuation ◽  
Robust Controller ◽  
Large Systems ◽  
Delay Dependent

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

Complex projection synchronization of fractional order uncertain complex-valued networks with time-varying coupling

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Dawei Ding ◽  
Xiaolei Yao ◽  
Hongwei Zhang
Keyword(s):  
Fractional Order ◽  
Coupling Strength ◽  
Dynamic Networks ◽  
Sufficient Conditions ◽  
Feedback Gain ◽  
Time Varying ◽  
Order Complex ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Complex Valued

In this paper, the complex projection synchronization problem of fractional complex-valued dynamic networks is investigated. Considering the time-varying coupling and unknown parameters of the fractional order complex network, several decentralized adaptive strategies are designed to adjust the coupling strength and controller feedback gain in order to investigate the complex projection synchronization problem of the system. Moreover, based on the designed identification law, the uncertain parameters in the network can be estimated. Using adaptive law which balances the time-varying coupling strength and the feedback gain of the controller, some sufficient conditions are obtained for the complex projection synchronization of complex networks. Finally, numerical simulation examples are provided to illustrate the efficiency of the complex projection synchronization strategies of the fractional order complex dynamic networks.

scholarly journals Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Quan Xu ◽  
Zilong Chen ◽  
Weifan Zheng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Homeomorphism Mapping ◽  
Complex Valued

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

An Asymptotical Stability in Variational Sense for Second Order Systems

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Dariusz Idczak ◽  
Stanisław Walczak
Keyword(s):  
Sobolev Space ◽  
Differential System ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Second Order ◽  
Functional Parameter ◽  
Asymptotical Stability ◽  
Parameter Control ◽  
Initial Condition ◽  
Second Order Systems

AbstractIn this paper, a new, variational concept of asymptotical stability of zero solution to an ordinary differential system of the second order, considered in Sobolev space, is presented. Sufficient conditions for an asymptotical stability in a variational sense with respect to initial condition and functional parameter (control) are given. Relation to the classical asymptotical stability is illustrated.

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