Delay-dependent LMI-based robust stability criterion for discrete and distributed time-delays Markovian jumping reaction–diffusion CGNNs under Neumann boundary value

Zhang, Pu; Rao, Ruizhong

doi:10.1016/j.neucom.2015.07.063

Cited by 14 publications

(15 citation statements)

References 28 publications

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“…As pointed out in [23], the delayed feedback coefficient has the Markov property, we may consider the Markovian jumping model for the delayed financial system. Motivated by some ideas and methods in related literature ( [3,5,7,[9][10][11][12][13][14][15][16][17][18][19][21][22][23][24][25][27][28][29][30][31][32][33][35][36][37]), we may consider employing regional control to derive the input-to-state stability criterion for the delayed feedback financial system with Markovian jumping. On the other hand, we consider using solely the impulse control to stabilize the delayed feedback financial system.…”

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confidence: 99%

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Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy

Rao¹,

Zhong²

2021

Discrete &Amp; Continuous Dynamical Systems - S

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The stochastic inflow or withdrawal of funds in the international financial market are both positive or negative external inputs to the domestic financial system. So, in this paper, input-to-state stability criterion of delayed feedback chaotic financial system is investigated, and derived by counterevidence method, Lyapunov functional method, variational method and regional control technique, which was involved to equilibrium solution with the positive interest rate. On the other hand, if these inputs are too small to be ignored, impulse control can be applied to stability analysis of the delayed feedback system, in which the delayed impulse allows the pulse effect to lag for a period of time. The obtained stability criteria show that no matter how complex and chaos the financial system is, high-frequency effective macro-control is conducive to the global asymptotical stability of the economic system, including the open economic model with foreign investment fund inputs. Finally, numerical examples illustrate the effectiveness of all the proposed methods.

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confidence: 99%

“…Let Y be a solution of the system (10). With the help of the Gauss formula, the zero boundary condition and the orthogonal decomposition of Sobolev space H 1 (Ω), the authors of [22] derived the following Poincare inequality :…”

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confidence: 99%

Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy

Rao¹,

Zhong²

2021

Discrete &Amp; Continuous Dynamical Systems - S

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“…There has always been a problem (see,e.g. Remark 8): whether is it the case in the literature( [1][2][3][4][5][6][7][8][9][10]) that the greater the diffusion, the more stable the system will be ? Now, our (3.35).…”

Section: * * )mentioning

confidence: 99%

“…For a long time, the stability of the reaction diffusion neural networks was investigated in many literatures [1][2][3][4][5][6][7][8][9][10], in which the stability of the constant equilibrium point was studied. For example, in [1], the following cellular neural networks with time-varying delays and reaction-diffusion terms was considered, Here, we have to say, the equilibrium point y * is also the equilibrium point of the following ordinary differential equations corresponding to the time-delayed partial differential equations (1.1), dx(t) dt = − Cx(t) + Ag(x(t)) + Bg(x(t − τ(t))) + J, t ∈ R + , (1.3) Due to the Poincare inequality, we see, the diffusion items actually promote the stability of the reaction diffusion system (1.1).…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks With Time Delays

Rao¹

2020

Preprint

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Firstly, the existence of asymptotically stable nontrivial stationary solution is derived by the comprehensive applications of Lyapunov-Razumikhin technique, design of state-dependent switching laws, a fixed point theorem, variational methods, and construction of compact operators on a convex set. This new theorem shows that the diffusion is a double-edged sword to the stability, refuting the views in previous literature that the greater the diffusion effect, the more stable the system will be. Next, a series of new theorems are presented one by one, which illustrates that the globally asymptotical stability of ordinary differential equations model for delayed neural networks may be locally stable in actual operation due to the inevitable diffusion. Besides, the non-zero constant equilibrium point is pointed out to be not the solution of delayed reaction diffusion system so that the stability of the non-zero constant equilibrium point of reaction diffusion system must lead to a contradiction. That is, non-zero constant equilibrium points are not in the phase plane of dynamic system. In addition, new theorems are further presented to prove that the small diffusion effect will cause the essential change of the phase plane structure of the dynamic behavior of the delayed neural networks, and thereby one equilibrium solution may become several stationary solutions, even infinitely many positive stationary solutions. Finally, a numerical example illustrates the feasibility of the proposed methods.

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“…Combined with a linear matrix inequality (LMI) approach [22], the Riccati matrix equations could be solved easily [23]. Several above references also indicated that a LMI approach was widely applied to analyze the stability of the control systems with time-delay [24,25] or design time-delay compensation controllers [26,27]. Although the timevarying delay compensation was considered in a GCC system [28], structural parametric uncertainties including stiffness and mass variations reduced the performance of the control system.…”

Section: Introductionmentioning

confidence: 99%

A State Feedback Controller Based on GCC Algorithm against Wind‐Induced Motion for High‐Rise Buildings with Parametric Uncertainties

Chen

Teng

et al. 2019

Shock and Vibration

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High-rise buildings with an active mass damper/driver (AMD) system generally use a simplified mathematical model. e result leads to parametric uncertainties including the stiffness and mass variations exist, and the accuracy of its controller is seriously affected. In view of the above uncertainties, based on a Lyapunov stability theory and linear matrix inequality (LMI) approach, a state feedback controller based on the guaranteed cost control (GCC) algorithm is proposed in this paper. A ten-storey frame with an AMD system is taken as a numerical example, and its control effect and AMD parameters are viewed as the control indexes. e performance of the proposed robust controller is compared with a conventional controller based on the classical LQR algorithm. e analysis results show that the new controller effectively suppresses the dynamic responses of high-rise buildings with parametric uncertainties and keeps the AMD parameters stable. Finally, a four-storey steel experimental frame with an AMD system is used to verify the correctness of the conclusions.

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Delay-dependent LMI-based robust stability criterion for discrete and distributed time-delays Markovian jumping reaction–diffusion CGNNs under Neumann boundary value

Cited by 14 publications

References 28 publications

Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy

Input-to-state stability and no-inputs stabilization of delayed feedback chaotic financial system involved in open and closed economy

Stability Analysis of Nontrivial Stationary Solution and Constant Equilibrium Point of Reaction-Diffusion Neural Networks With Time Delays

A State Feedback Controller Based on GCC Algorithm against Wind‐Induced Motion for High‐Rise Buildings with Parametric Uncertainties

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