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Related Concept Videos

State Space Representation01:27

State Space Representation

316
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
316
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

133
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
133
Linear time-invariant Systems01:23

Linear time-invariant Systems

499
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
499
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

558
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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....
558
State Space to Transfer Function01:21

State Space to Transfer Function

333
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
333
Transfer Function to State Space01:23

Transfer Function to State Space

438
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
438

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Synchronization and state estimation for discrete-time coupled delayed complex-valued neural networks with random

Yufei Liu1, Bo Shen1, Ping Zhang2

  • 1College of Information Science and Technology, Donghua University, Shanghai 201620, China; Engineering Research Center of Digitalized Textile and Fashion Technology, Ministry of Education, Shanghai 201620, China.

Neural Networks : the Official Journal of the International Neural Network Society
|March 22, 2022
PubMed
Summary

This study addresses synchronization and state estimation for complex-valued neural networks (CVNNs) with random parameters and delays. Novel criteria ensure mean-square asymptotic stability for synchronization and state estimation in these networks.

Keywords:
Coupled complex-valued neural networksDiscrete-timeRandom system parametersState estimationSynchronization

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Area of Science:

  • Complex-valued neural networks
  • Nonlinear systems theory
  • Stochastic systems

Background:

  • Coupled complex-valued neural networks (CVNNs) are crucial for complex data processing.
  • Real-world CVNNs often exhibit random system parameters and time-varying delays.
  • Ensuring synchronization and accurate state estimation in such networks is challenging.

Purpose of the Study:

  • To develop methods for synchronization of discrete-time coupled CVNNs with random parameters and delays.
  • To design a state estimator for identical coupled CVNNs with stochastic parameters and time delays.
  • To guarantee mean-square asymptotic stability for both synchronization and state estimation problems.

Main Methods:

  • Lyapunov stability theory and Kronecker product for synchronization analysis.
  • Development of a suitable Lyapunov functional for state estimation.
  • Stochastic analysis to handle random system parameters.
  • Design of a state estimator based on derived stability conditions.

Main Results:

  • A synchronization criterion is proposed, guaranteeing mean-square asymptotic synchronization.
  • Sufficient conditions for the mean-square asymptotic stability of the estimation error system are derived.
  • An explicit design scheme for the state estimator is provided.
  • Numerical simulations validate the theoretical findings.

Conclusions:

  • The proposed methods effectively achieve synchronization and state estimation for discrete-time coupled CVNNs with random parameters and delays.
  • The derived criteria ensure the desired stability properties in the mean square.
  • The study provides a robust framework for analyzing and designing complex neural network systems.