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BIBO stability of continuous and discrete -time systems01:24

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.
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....
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An ecological disturbance is a temporary disruption in the environment resulting from abiotic, biotic, or anthropogenic factors, causing a pronounced change in an ecosystem. The impact of an ecological disturbance, which can depend on its intensity, frequency, and spatial distribution, plays a significant role in shaping the species diversity within the ecosystem.
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The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
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Discrete-Time Fourier Series01:20

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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
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Control systems are everywhere in contemporary society, influencing diverse applications from aerospace to automated manufacturing. These systems can be found naturally within biological processes, such as blood sugar regulation and heart rate adjustment in response to stress, as well as in man-made systems like elevators and automated vehicles. A control system is essentially a network of subsystems and processes that collaboratively convert specific inputs into desired outputs.
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Related Experiment Video

Updated: Jan 19, 2026

BIBO stability of continuous and discrete -time systems
01:24

BIBO stability of continuous and discrete -time systems

889

Observer-Based Event-Driven Control for Discrete-Time Systems With Disturbance Rejection.

Jinhui Zhang, Wei Xing Zheng, Hao Xu

    IEEE Transactions on Cybernetics
    |September 13, 2019
    PubMed
    Summary

    This study introduces event-driven control for discrete-time systems, reducing controller updates while effectively rejecting disturbances using extended state observers (ESOs). The proposed method enhances system performance by estimating and compensating for disturbances in real-time.

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    Area of Science:

    • Control Systems Engineering
    • Discrete-Time Systems Analysis
    • Observer-Based Control

    Background:

    • Disturbance rejection is critical for robust control of discrete-time systems.
    • Event-driven control offers potential for reduced computational load compared to time-driven approaches.
    • Extended State Observers (ESOs) are effective for estimating unknown states and disturbances.

    Purpose of the Study:

    • To design event-driven output feedback controllers for disturbance rejection in discrete-time systems.
    • To investigate the use of full- and reduced-order Extended State Observers (ESOs) within an event-driven framework.
    • To analyze the stability and disturbance rejection performance of the proposed control strategy.

    Main Methods:

    • Design of event-driven schedulers for controller updates.
    • Development of full- and reduced-order Extended State Observers (ESOs) for state and disturbance estimation.
    • Construction of output feedback controllers utilizing estimated states and disturbances.
    • Stability and disturbance rejection analysis.

    Main Results:

    • Event-driven control significantly reduces controller updating frequency.
    • The proposed ESOs accurately estimate system states and external disturbances.
    • Effective disturbance compensation is achieved in the system's output channels.
    • Numerical simulations validate the efficacy of the developed control approaches.

    Conclusions:

    • Event-driven control frameworks, combined with ESOs, provide an effective strategy for disturbance rejection in discrete-time systems.
    • The proposed method enhances control efficiency by reducing computational requirements.
    • The approach demonstrates robustness in compensating for disturbances, validated by simulation results.