Finite-Time Boundedness of Impulsive Delayed Reaction–Diffusion Stochastic Neural Networks

Considering the impulsive delayed reaction&amp;#x2013;diffusion stochastic neural networks (IDRDSNNs) with hybrid impulses, the finite-time boundedness (FTB) and finite-time contractive boundedness (FTCB) are investigated in this article. First, a novel delay integral inequality is presented. By integrating this inequality with the comparison principle, some sufficient conditions that ensure the FTB and FTCB of IDRDSNNs are obtained. This study demonstrates that the FTB of neural networks with hybrid impulses can be maintained, even in the presence of impulsive perturbations. And for a system that is not FTB due to impulsive perturbations, achieving FTB is possible through the implementation of appropriate impulsive control and optimization of the average impulsive intervals. In addition, to validate the practicality of our results, three illustrative examples are provided. In the end, these theoretical findings are successfully applied to image encryption.</p

Finite-Time Boundedness of Impulsive Delayed Reaction–Diffusion Stochastic Neural Networks

Considering the impulsive delayed reaction&amp;#x2013;diffusion stochastic neural networks (IDRDSNNs) with hybrid impulses, the finite-time boundedness (FTB) and finite-time contractive boundedness (FTCB) are investigated in this article. First, a novel delay integral inequality is presented. By integrating this inequality with the comparison principle, some sufficient conditions that ensure the FTB and FTCB of IDRDSNNs are obtained. This study demonstrates that the FTB of neural networks with hybrid impulses can be maintained, even in the presence of impulsive perturbations. And for a system that is not FTB due to impulsive perturbations, achieving FTB is possible through the implementation of appropriate impulsive control and optimization of the average impulsive intervals. In addition, to validate the practicality of our results, three illustrative examples are provided. In the end, these theoretical findings are successfully applied to image encryption.</p

On hyper-exponential output-feedback stabilization of a double integrator by using artificial delay

International audienceThe problem of output-feedback stabilization of a double integrator is revisited with the objective of achieving the rates of convergence faster than exponential. It is assumed that only position is available for measurements, and the designed feedback is based on the output and its delayed values without an estimation of velocity. It is shown that by selecting the closed-loop system to be homogeneous with negative or positive degree it is possible to accelerate the rate of convergence in the system at the price of a small steady-state error. Efficiency of the proposed control is demonstrated in simulations

On output-based accelerated stabilization of a chain of integrators: Implicit Lyapunov-Krasovskii functional approach

International audienceThe problem of output accelerated stabilization of a chain of integrators is considered. Proposed control law nonlinearly depends on the output and its delayed values, and it does not use an observer to estimate the unmeasured components of the state. It is proven that such a nonlinear delayed control law ensures practical output stabilization with rates of convergence faster than exponential. The effective way of computation of feedback gains is given. It is shown that closed-loop system stability does not depend on the value of artificial delay, but the maximum value of delay determines the width of stability zone. The efficiency of the proposed control is demonstrated in simulations

Homogeneity of neutral systems and accelerated stabilization of a double integrator by measurement of its position

International audienceA new theory of homogeneity for neutral type systems with application to fast stabilization of the 2nd-order integrator is proposed. It is assumed that only the position is available for measurements, and the designed feedback uses the output and its delayed values without an estimation of velocity. It is shown that by selecting the closed-loop system to be homogeneous with negative or positive degree, it is possible to accelerate the rate of convergence in the system at the price of a small steady-state error. Robustness of the developed stabilization strategy with respect to exogenous perturbations is investigated. The efficiency of the proposed control is demonstrated in simulations

Fast Control Systems: Nonlinear Approach

International audienceThis chapter treats the problem of fast control design for nonlinear systems. First, we discusses the question: which nonlinear system can be called fast? Next, we develop some tools for analysis and design of such control systems. The method generalized homogeneity is mainly utilized for these purposes. Finally, we survey possible research directions of the fast control systems

Comments on Finite-time Stability of Time-Delay Systems

International audienceRecently proposed conditions on finite-time stability in time-delay systems are revisited and it is shown that they are incorrect. General comments on possibility of finite-time convergence in time-delay systems and a necessary condition are given