Related Experiment Videos
Global exponential stability of generalized recurrent neural networks with discrete and distributed delays
Yurong Liu1, Zidong Wang, Xiaohui Liu
1Department of Mathematics, Yangzhou University, Yangzhou 225002, People's Republic of China.
Abstract:
This paper is concerned with analysis problem for the global exponential stability of a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, by employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally exponentially stable. Therefore, the global exponential stability of the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.
Related Concept Videos
Multimachine Stability
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Exponential Equations for Modeling Growth
Classification of Systems-II
Transient and Steady-state Response
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state response.
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.