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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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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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Quantized filtering for T-S fuzzy networked systems with saturation nonlinearities: An output-dependent triggering

Yushun Tan1, Dongsheng Du2, Shumin Fei3

  • 1Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210023, PR China; School of Automation, Southeast University, Nanjing, Jiangsu 210096, PR China.

ISA Transactions
|November 22, 2017
PubMed
Summary

This study introduces an output-dependent triggering scheme and quantizer for H∞ filter design in fuzzy systems with saturation. This approach reduces network load while ensuring system stability and performance.

Keywords:
Fuzzy networked systemsH∞ filteringOutput-dependent triggering schemeSaturation nonlinearities

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Area of Science:

  • Control Systems Engineering
  • Fuzzy Logic Systems
  • Nonlinear Systems Analysis

Background:

  • Networked control systems often face communication constraints, necessitating efficient data transmission strategies.
  • Saturation nonlinearities are prevalent in physical systems, impacting filter performance and stability.
  • Designing robust H∞ filters for complex systems like Takagi-Sugeno (T-S) fuzzy models with these challenges is crucial.

Purpose of the Study:

  • To develop an H∞ filter design methodology for T-S fuzzy systems incorporating saturation nonlinearities.
  • To introduce an output-dependent triggering scheme and a quantizer to minimize network burden.
  • To establish sufficient conditions for filter existence and derive a co-design algorithm for the filter and event generator.

Main Methods:

  • Utilizing a Lyapunov functional approach combined with stochastic analysis techniques.
  • Formulating a filtering error model that accounts for saturation nonlinearities and the triggering/quantization scheme.
  • Deriving matrix inequality-based conditions for guaranteed filter performance.

Main Results:

  • Sufficient conditions for the existence of the designed H∞ fuzzy filter were established.
  • A novel co-design algorithm was developed to simultaneously determine the filter parameters and the event generator.
  • The effectiveness of the proposed approach was validated through a numerical example.

Conclusions:

  • The proposed output-dependent triggering and quantization scheme effectively reduces network load for H∞ filter design in T-S fuzzy systems with saturation.
  • The developed Lyapunov-based method and co-design algorithm provide a robust framework for addressing these complex filtering problems.
  • The numerical results confirm the practical applicability and performance of the proposed filtering strategy.