Vector Lyapunov-like functions for multi-order fractional systems with multiple time-varying delays (original) (raw)

On the Asymptotic Stability of a Nonlinear Fractional-order System with Multiple Variable Delays

2020

In this paper, we consider a nonlinear differential system of fractional-order with multiple variable delays. We investigate asymptotic stability of zero solution of the considered system. We prove a new result, which includes sufficient conditions, on the subject by means of a suitable Lyapunov functional. An example with numerical simulation of its solutions is given to illustrate that the proposed method is flexible and efficient in terms of computation and to demonstrate the feasibility of established conditions by MATLAB-Simulink

Stability and Stabilization of Linear Fractional Order Systems with Input Delay Using Linear Matrix Inequalities

2017

Stability and stabilization of delayed linear fractional order systems with input delay using linear matrix inequalities were considered in the present study. At first, the input delay fractional order system was changed into a free delay fractional order system using an alternate variable. Thereafter, using a state feedback, the systems were turned into a closed loop. Later on, the system stabilization was examined by applying linear matrix inequality theorems and, finally, an example was used to demonstrate the efficiency of the proposed method.

Stability conditions for fractional-order linear equations with delays

DOAJ (DOAJ: Directory of Open Access Journals), 2018

The problem of stability of the Grünwald-Letnikov-type linear fractional-order discrete-time systems with delays is discussed. For the stability analysis of the considered systems the Z-transform is used. The sufficient conditions for the asymptotic stability of the considered systems are presented. Using conditions related to eigenvalues of the matrices defining the linear difference systems, one can determine the regions of location of eigenvalues of matrices associated to the systems in order to guarantee the asymptotic stability of the considered systems. Some of these regions are illustrated with relevant examples.

Asymptotical stability of fractional order systems with time delay via an integral inequality

IET Control Theory & Applications

In this paper, the asymptotical stability for several classes of fractional order differential systems with time delay is investigated. We firstly present an integral inequality by which the Halanay inequality is extended to fractional order case. Based on the generalized Halanay inequality, we establish several asymptotical stability conditions under which the fractional order systems with time delay are asymptotically stable. It is worth to note that these stability conditions are easy to check without resorting to the solution expression of the systems.

Stability analysis of linear distributed order fractional systems with distributed delays

Fractional Calculus and Applied Analysis

In the present work we study linear systems with distributed delays and distributed order fractional derivatives based on Caputo type single fractional derivatives, with respect to a nonnegative density function. For the initial problem of this kind of systems, existence, uniqueness and a priory estimate of the solution are proved. As an application of the obtained results, we establish sufficient conditions for global asymptotic stability of the zero solution of the investigated types of systems.

Some Fractional Comparison Results and Stability Theorem for Fractional Time Delay Systems

In this paper, we have investigated that boundedness criteria and Lyapunov stability for fractional order time delay systems (fractional order differentialdifference equations) in Caputo's sense are unified with Lyapunov-like functions to establish comparison result. The qualitative behaviour of a fractional order time-delay differential equation with Caputo's derivative has been studied. We present some new comparison results that again give the null solution a central role in the comparison fractional order differential systems with delay when establishing boundedness criteria and Lyapunov stability of these systems in Caputo's sense.

Robust Output Feedback Control for Fractional Order Nonlinear Systems with Time-varying Delays

Robust controller design problem is investigated for a class of fractional order nonlinear systems with time varying delays. Firstly, a reduced-order observer is designed. Then, an output feedback controller is designed. Both the designed observer and controller are independent of time delays. By choosing appropriate Lyapunov functions, we prove the designed controller can render the fractional order system asymptotically stable. A simulation example is given to verify the effectiveness of the proposed approach. Citation: Changchun Hua, Tong Zhang, Yafeng Li, Xinping Guan. Robust output feedback control for fractional order nonlinear systems with time-varying delays. IEEE/CAA Journal of Automatica Sinica, 2016, 3(4): 477-482

Robust finite-time stability analysis of fractional order time delay systems: New results

In this paper, a stability test procedure is proposed for perturbed nonlinear nonhomogeneous fractional order systems with a pure time delay. Sufficient conditions of this kind of stability are derived for particular class of fractional time-delay systems using generalized Gronwall inequality. A numerical example is given to illustrate the validity of the proposed procedure.