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BIBO stability of continuous and discrete -time systems

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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.
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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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Linear time-invariant Systems01:23

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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.
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Ultimately Bounded Filtering for Time-Delayed Nonlinear Stochastic Systems with Uniform Quantizations under Random

Jiyue Guo1, Zidong Wang1,2, Lei Zou2

  • 1College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China.

Sensors (Basel, Switzerland)
|July 30, 2020
PubMed
Summary
This summary is machine-generated.

This study addresses filtering for nonlinear stochastic systems with time delays, random access protocols (RAP), and uniform quantization effects (UQEs). A novel nonlinear filter is designed to ensure exponential ultimate boundedness in mean square for the filtering error dynamics.

Keywords:
discrete-time systemsrandom access protocoltime-delaysultimately bounded filteringuniform quantization

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Area of Science:

  • Control Systems Engineering
  • Stochastic Systems Analysis
  • Nonlinear Dynamics

Background:

  • Investigates filtering for nonlinear stochastic systems with time delays.
  • Addresses challenges posed by random access protocols (RAP) and uniform quantization effects (UQEs) in data transmission.
  • Considers the Markovian nature of RAP scheduling for system modeling.

Purpose of the Study:

  • To devise a nonlinear filter for time-delay nonlinear stochastic systems.
  • To ensure the filtering error dynamics are exponentially ultimately bounded in mean square (EUBMS) under RAP and UQEs.
  • To present a filter design algorithm based on derived sufficient conditions.

Main Methods:

  • Employs stochastic analysis techniques.
  • Utilizes Lyapunov stability theory for system analysis.
  • Characterizes RAP scheduling using a Markov chain with known transition probabilities.

Main Results:

  • Derives sufficient conditions for the existence of the desired nonlinear filter.
  • Presents a concrete algorithm for designing the nonlinear filter.
  • Demonstrates the effectiveness of the proposed filtering strategy through two simulation examples.

Conclusions:

  • The proposed nonlinear filter effectively manages filtering errors in systems with time delays, RAP, and UQEs.
  • The theoretical conditions and design algorithm provide a robust framework for practical applications.
  • Simulation results validate the performance and applicability of the developed filtering strategy.