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Related Concept Videos

Linear time-invariant Systems

Linear time-invariant Systems

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 calculated...

Feedback control systems

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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.

State Space Representation

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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.
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The fast decoupled power flow method addresses contingencies in power system operations, such as generator outages or transmission line failures. This method provides quick power flow solutions, essential for real-time system adjustments. Fast decoupled power flow algorithms simplify the Jacobian matrix by neglecting certain elements, leading to two sets of decoupled equations:

Linear Approximation in Time Domain

Linear Approximation in Time Domain

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.
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Related Experiment Videos

Decentralized fuzzy Hinfinity filtering for nonlinear interconnected systems with multiple time delays.

Hongbin Zhang¹, Chuangyin Dang, Jian Zhang

¹School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China. zhanghb@uestc.edu.cn

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society

|April 6, 2010

Summary

Designing decentralized H-infinity fuzzy filters for nonlinear systems with time delays is challenging. This study presents a novel approach using Takagi-Sugeno (T-S) fuzzy models to ensure stability and performance for interconnected systems.

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Area of Science:

Control Systems Engineering
Fuzzy Logic Systems
Nonlinear System Analysis

Background:

Designing H-infinity filters for nonlinear interconnected systems is complex due to subsystem interactions.
Multiple time delays further complicate filter design in these systems.

Purpose of the Study:

To introduce a decentralized H-infinity fuzzy filter design for nonlinear interconnected systems with multiple time delays.
To ensure asymptotic stability and a prescribed H-infinity performance index for the filtering error system.

Main Methods:

Utilizing Takagi-Sugeno (T-S) fuzzy models, specifically N time-delay T-S fuzzy subsystems.
Developing a decentralized H-infinity filter based on the T-S fuzzy model.
Establishing a sufficient condition for filter existence using numerically feasible linear matrix inequalities (LMIs).

Main Results:

The proposed decentralized filter guarantees asymptotic stability for the overall filtering error system.
A prescribed H-infinity performance index is achieved for the filtering error.
The method's effectiveness is demonstrated through a simulation example.

Conclusions:

The presented decentralized H-infinity fuzzy filter design is effective for nonlinear interconnected systems with time delays.
The use of T-S fuzzy models and LMIs provides a feasible and robust solution.
This approach offers a valuable tool for robust filtering in complex dynamic systems.