Controllability Results for Nonlinear Fractional-Order Dynamical Systems

On fractional order adaptive observer

“…Theorem 1. For plant (6), if the adaptive observer is designed as (8), (10) and (25), then all the signals in the closed-loop adaptive system are global uniformly bounded. And if u(t) can guarantee that φ (t) is persistent excitation, then the parameter estimation and state observation are achieved as…”

“…Due to more and more scholars devoting themselves to the fractional order field, a tremendous amount of valuable results on system identification [3,4] , controllability and observability [5,6] , stability analysis [7−9] and controller synthesis [10−12] of fractional order systems have been reported in the literature. Many fundamentals and applications of fractional order control systems can be found in [3] and the reference therein.…”

Controllability result of nonlinear higher order fractional damped dynamical system

“…The various types of fractional differential equation, playing significant roles and tools, are used for solving some mathematical issues of general physical phenomena in physics and engineering. Especially, the field of control theory sparked the interest of many scholars which can be seen from the literatures [10,19,25]. In recent years, several authors [8, 11-13, 15, 17] have made a detailed research about controllability results of linear and proposed many new ideas about the low-order fractional equation.…”

Controllability of fractional damped dynamical systems

“…On the other hand, control system is an interconnection of components forming a system configuration that will provide a desired system response. Recently Balachandran et al [25][26][27] established the controllability results for fractional oscillator type dynamical systems by using fixed point theorems and iterative technique.…”