Browsing by Author "a85bb483-5fdb-4b94-b901-a5dd1e542377"

Now showing items 1-11 of 11

    • Convergence of fractional adaptive systems using gradient approach 
      Gallegos, Javier A.; Duarte Mermoud, Manuel (Elsevier, 2017)
      Conditions for boundedness and convergence of the output error and the parameter error for various Caputo's fractional order adaptive schemes based on the steepest descent method are derived in this paper. To this aim, the ...
    • Converse theorems in Lyapunov's second method and applications for fractional order systems 
      Gallegos, Javier A.; Duarte-Mermoud, Manuel A. (TUBITAK, 2019)
      We establish a characterization of the Lyapunov and Mittag-Leffler stability through (fractional) Lyapunov functions, by proving converse theorems for Caputo fractional order systems. A hierarchy for the Mittag-Leffler ...
    • Mixed order fractional observers for minimal realizations of linear time-invariant systems 
      Duarte-Mermoud, Manuel; Gallegos, Javier; Aguila Camacho, Norelys; Castro-Linares, Rafael (MDPI AG, 2018)
      Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. ...
    • Mixed order robust adaptive control for general linear time invariant systems 
      Gallegos, Javier A.; Duarte Mermoud, Manuel; Castro-Linares, Rafael (Elsevier, 2018-05)
      We provide a solution to the adaptive control problem of an unknown linear system of a given derivation order, using a reference model or desired poles defined in a possibly different derivation order and employing continuous ...
    • On the Lyapunov theory for fractional order systems 
      Gallegos, Javier A.; Duarte Mermoud, Manuel (Elsevier, 2016)
      We provide the main features of Lyapunov theory when it is formulated for fractional order systems. We give consistent extensions of Lyapunov, LaSalle and Chetaev classical theorems to the case of fractional order systems. ...
    • Robust adaptive passivity-based (PID)-D-lambda control 
      Gallegos, Javier A.; Águila Camacho, Norelys; Duarte Mermoud, Manuel (Wiley, 2020)
      In this article, we develop proportional, fractional-integral, and derivative (PI lambda D) controllers for the regulation and tracking problems of nonlinear systems. The analytic results are obtained by extending the ...
    • Robust mixed order backstepping control of non-linear systems 
      Gallegos, Javier A.; Duarte Mermoud, Manuel (Institution of Engineering and Technology, 2018-06-12)
      Robust backstepping control of non-linear systems with derivation orders (commensurate or non-commensurate) lying at interval (0, 2) is proposed in this study. The stability and robustness properties are proved using a ...
    • Robustness and convergence of fractional systems and their applications to adaptive schemes 
      Gallegos, Javier A.; Duarte Mermoud, Manuel (De Gruyter, 2017)
      Our general aim is to give sufficient conditions for robustness behavior and convergence to the equilibrium point of linear time-varying fractional system's solutions. We approach this problem using as a framework a series ...
    • Smooth solutions to mixed-order fractional differential systems with applications to stability analysis 
      Gallegos, Javier A.; Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A. (Rocky Mountain Mathematics Consortium, 2019)
      Conditions for existence, uniqueness and smoothness of solutions for systems of fractional differential equations of Caputo and/or Riemann-Liouville type having all of them in general and not of the same derivation order ...
    • Sufficient condition on the fractional integral for the convergence of a function 
      Duarte-Mermoud, Manuel A.; Aguila-Camacho, Norelys; Gallegos, Javier A. (2013)
      A sufficient condition on the fractional integral of the absolute value of a function is given in this paper, which allows to assure the convergence of the function to zero. This result can be useful to assure the convergence ...
    • Vector Lyapunov-like functions for multi-order fractional systems with multiple time-varying delays 
      Gallegos, Javier A.; Aguila Camacho, Norelys; Duarte Mermoud, Manuel (Elsevier, 2020)
      In this paper, a general method to establish the asymptotic behaviour of solutions to multi-order multiple time-varying delays nonlinear systems is proposed. The method, relying on vector Lyapunov-like functions and on ...