On Observer Design for Nonlinear Caputo Fractional‐Order Systems

Abstract

The observer design problem for integer-order systems has been the subject of several studies. However, much less interest has been given to the more general fractional-order systems, where the fractional-order derivative is between 0 and 1. In this paper, a particular form of observers for integer-order Lipschitz, one-sided Lipschitz and quasi-one-sided Lipschitz systems, is extended to the fractional-order calculus. Then, the obtained states estimates are used for an eventual feedback control, and the separation principle is tackled. The effectiveness of the proposed scheme is shown through simulation for two numerical examples.

Coexisting attractors in a fractional order hydro turbine governing system and fuzzy PID based chaos control

“…Most prior studies have used the Caputo method for numerical solutions of the fractional order systems 34 . It has been shown that the GL method to solve fractional order systems has smoothness over other methods (due to the smoothness in the coefficients) 35, 36 .…”

Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input

“…For stability and stabilization of fractional-order systems we refer to the series of papers. [7][8][9][10] Recently, Lyapunov stability theory and Razumikhin method were modified and applied to fractional systems with time dependent delays in The analysis of bounded input bounded output (BIBO) stability of systems is very important for its possible application in many aspects such as single/double-loop modulators, or issues connected with bilinear input/output maps, and so forth. The BIBO stability for 2D discrete delayed systems is studied in Reference 14, for networked control systems with short time-varying delays in Reference 15, for retarded systems in Reference 16, for switched uncertain neutral systems with constant delay is considered in Reference 17, for perturbed interconnected power systems in Reference 18, for feedback control system with time delays, 2 and for Lurie system with time-varying delay in Reference 19.…”

“…In engineering, for example, the digital fractional‐order controller was designed to control temperature in Reference 4, the fractional‐order PID controller was used in Reference 5 to control the trajectory of the flight path and stabilization of a fractional‐order time delay nonlinear systems in Reference 6. For stability and stabilization of fractional‐order systems we refer to the series of papers 7‐10 …”

Stability analysis and robust synchronization of fractional‐order competitive neural networks with different time scales and impulsive perturbations

“…[28][29][30][31][32][33][34] So, dynamical behavior of the fractional-order systems based on fractional-order calculation is very significant, and some excellent results have been demonstrated. [35][36][37] The further study of fractional derivatives is needed to an essential issue of its widespread application in the stability, stabilization, Chao's synchronization, control theory, etc. For example, Liao and Huang 38 demonstrated the chaotic synchronization of nonlinear systems and its application to secure communications based on observer-based approaches.…”