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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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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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Performance analysis for interconnected time-delay systems with networked communication.

Dan Zhang1, Huiling Xu1, Hui Wang1

  • 1School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu, 210094, China.

ISA Transactions
|February 27, 2022
PubMed
Summary
This summary is machine-generated.

This study analyzes interconnected time-delay systems (ITDS) with network delays. New methods ensure system stability despite network imperfections, offering practical computational conditions.

Keywords:
Hybrid systems with memoryInterconnected time-delay systemPacket-based communication networkStability analysis

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Area of Science:

  • Control Theory
  • Systems Engineering
  • Networked Systems

Background:

  • Interconnected time-delay systems (ITDS) face performance degradation due to state delays and packet-based communication.
  • Network-induced imperfections, such as delays, complicate the analysis and control of these systems.
  • Existing models often struggle to unify delay and network effects.

Purpose of the Study:

  • To develop a unified framework for analyzing networked ITDS with state and communication delays.
  • To propose stability conditions that are computationally feasible.
  • To demonstrate the applicability of the proposed methods through examples.

Main Methods:

  • Modeling ITDS with networked communication as hybrid systems with memory.
  • Construction of a general hybrid Lyapunov-Krasovskii functional.
  • Derivation of sufficient linear matrix inequality (LMI) conditions for asymptotic and L2 stability.

Main Results:

  • Proposed LMI conditions for ITDS stability, considering interconnected structure and local network parameters.
  • Conditions are independent of subsystem interconnections, simplifying computation.
  • Demonstrated feasibility and effectiveness using a numerical example and a power system.

Conclusions:

  • The developed framework effectively addresses stability analysis for networked ITDS with time delays.
  • The proposed LMI conditions provide a practical tool for assessing system stability.
  • The results are applicable to complex systems like power grids with networked control.