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Related Concept Videos

State Space Representation01:27

State Space Representation

420
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...
420
Linear time-invariant Systems01:23

Linear time-invariant Systems

725
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...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

791
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....
791
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

234
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,...
234
First Order Systems01:21

First Order Systems

283
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
283
Transfer Function to State Space01:23

Transfer Function to State Space

630
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 RLC...
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Related Experiment Video

Updated: Dec 5, 2025

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Finite-Time H∞ State Estimation for Two-Time-Scale Complex Networks Under Stochastic Communication Protocol.

Xiongbo Wan, Yongzhi Li, Yuqing Li

    IEEE Transactions on Neural Networks and Learning Systems
    |October 14, 2020
    PubMed
    Summary

    This study develops finite-time H∞ state estimation for nonlinear two-time-scale complex networks using a stochastic communication protocol. The method ensures bounded error dynamics and optimal performance despite unknown transmission probabilities.

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    Area of Science:

    • Control Systems Engineering
    • Networked Systems
    • Nonlinear Dynamics

    Background:

    • Complex networks exhibit multi-time-scale dynamics.
    • State estimation in networked systems faces challenges like limited bandwidth and data collisions.
    • H∞ control provides robustness against disturbances.

    Purpose of the Study:

    • To design a finite-time H∞ state estimator for discrete-time nonlinear two-time-scale complex networks (TTSCNs).
    • To address state estimation under a stochastic communication protocol (SCP) over bandwidth-limited channels.
    • To account for state evolutions at different time scales using a singular perturbation parameter (SPP).

    Main Methods:

    • A new discrete-time TTSCN model incorporating an SPP is developed.
    • A stochastic communication protocol (SCP) is employed to manage data transmissions and mitigate collisions.
    • A novel Lyapunov function, considering SCP and SPP, is constructed to analyze error dynamics.

    Main Results:

    • A sufficient condition is derived to guarantee stochastically finite-time boundedness of the error dynamics.
    • The derived condition ensures the state estimation satisfies a prescribed H∞ performance index.
    • Gain matrices for the state estimator are determined via matrix inequalities, and the admissible SPP upper bound is evaluated.

    Conclusions:

    • The proposed finite-time H∞ state estimation method is effective for discrete-time nonlinear TTSCNs under SCP.
    • The approach provides robust performance and boundedness guarantees in the presence of communication uncertainties.
    • The study demonstrates the practical applicability through illustrative examples.