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Adaptive state-dependent impulsive observer design for nonlinear deterministic and stochastic dynamics with

Nasrin Kalamian1, Hamid Khaloozadeh1, S Moosa Ayati2

  • 1Department of Systems and Control Engineering, K.N. Toosi University of Technology, Tehran, Iran.

ISA Transactions
|September 8, 2019
PubMed
Summary

A new adaptive state-dependent impulsive observer (ASDIO) effectively controls nonlinear systems with time-varying delays. This observer ensures state and parameter estimation errors approach zero, even for complex stochastic systems.

Keywords:
Adaptive state-dependent impulsive observerComparison system theoryExtended pseudo-linearizationLinear matrix inequalityNonlinear deterministic and stochastic systems with time-delay

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Impulsive Systems

Background:

  • Controlling nonlinear systems with time-varying delays presents significant challenges.
  • Existing methods may not adequately address systems with distributed, multiple, or state-dependent delays.

Purpose of the Study:

  • Introduce a novel adaptive state-dependent impulsive observer (ASDIO).
  • Ensure the stability and performance of the observer for nonlinear systems with time-varying delays.
  • Extend the observer's applicability to stochastic nonlinear systems.

Main Methods:

  • Extended pseudo-linearization to parameterize nonlinear systems.
  • Time-varying and delay-independent Lyapunov functional approach.
  • Comparison method for impulsive and stochastic impulsive systems.

Main Results:

  • The ASDIO is applicable to nonlinear systems with distributed, multiple, and time-varying delays.
  • Stability analysis confirmed state and parameter estimation errors asymptotically approach zero.
  • New theorems provided less-conservative conditions for stability and specified maximum impulse time.

Conclusions:

  • The proposed ASDIO offers a robust solution for controlling complex nonlinear systems with time-varying delays.
  • The observer demonstrates effectiveness for both deterministic and stochastic systems.
  • Simulation on an epidemic system validated the observer's practical performance.