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Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications.

Xiaoxiao Lv1, Xiaodi Li2

  • 1School of Mathematics and Statistics, Shandong Normal University, Ji'nan, 250014, PR China.

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Summary

This study introduces new criteria for finite time stability (FTS) in nonlinear impulsive sampled-data systems. The methods provide less conservative results for designing hybrid controllers, improving system predictability.

Keywords:
Finite time stability (FTS)ImpulseLinear matrix inequality (LMI)Nonlinear systemsSampled-data control

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Systems Theory

Background:

  • Impulsive systems and sampled-data systems present unique control challenges.
  • Ensuring finite time stability (FTS) is crucial for predictable system behavior.
  • Existing methods for analyzing these systems can be conservative.

Purpose of the Study:

  • To develop novel finite time stability (FTS) criteria for nonlinear impulsive sampled-data systems.
  • To design a hybrid controller incorporating both sampled-data and impulsive control strategies.
  • To reduce conservatism in stability analysis for these complex systems.

Main Methods:

  • Construction of a specialized Lyapunov function.
  • Application of the average impulsive interval (AII) method.
  • Derivation of stability criteria using linear matrix inequalities (LMIs).

Main Results:

  • New FTS criteria for nonlinear impulsive sampled-data systems were established.
  • The derived criteria are expressed in easily verifiable LMIs.
  • The proposed criteria are shown to be less conservative than existing methods.
  • A hybrid controller was designed using the LMIs.

Conclusions:

  • The developed FTS criteria offer a less conservative approach for nonlinear impulsive sampled-data systems.
  • The LMI-based approach facilitates practical controller design and verification.
  • The findings contribute to the advancement of robust control strategies for complex dynamic systems.