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Chellaboina, V., Bhat, S.P. and Haddad, W.M. (2003) An Invariance Principle for Nonlinear Hybrid and Impulsive Dynamical Systems. Nonlinear Analysis: Theory, Methods & Applications, 53, 527-550.
https://doi.org/10.1016/s0362-546x(02)00316-4

has been cited by the following article:

• TITLE: Application of Stability Criteria for Complex-Valued Impulsive System by Lyapunov Function

  AUTHORS: Wei Yang

  KEYWORDS: Complex-Valued Systems, Stability, Lyapunov Function, Impulsive Control Field

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.13 No.4, December 17, 2024

  ABSTRACT: Stability criteria for the complex-valued impulsive system are applied widely in many fields, such as quantum systems, which have been studied in recent decades. In this paper, I investigate the Lyapunov control of finite dimensional complex-valued systems with impulsive control fields, where the studied complex-valued systems are governed by the Schrödinger equation and can be used in quantum systems. By one Lyapunov function based on state error and the invariant principle of impulsive systems, I study the convergence of complex-valued systems with impulsive control fields and propose new results for the mentioned complex-valued systems in the form of sufficient conditions. A numerical simulation to validate the proposed control method is provided.