Related papers: Fractional Order Hybrid Systems and Their Stabilit…
This paper is concerned with the stabilization problem of singular fractional order systems with order $\alpha\in(0,2)$. In addition to the sufficient and necessary condition for observer based control, a sufficient and necessary condition…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space…
We study the stability of linear fractional order maps. We show that in the stable region, the evolution is described by Mittag-Leffler functions and a well defined effective Lyapunov exponent can be obtained in these cases. For…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
In this paper, we study a class of multi-order fractional nonlinear delay systems. Our main contribution is to show the (local or global) Mittag-Leffler stability of systems when some structural assumptions are imposed on the "vector…
The article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models viz. Fractional continuously variable order mass-spring damper systems. Here, we use the…
In this paper, fractional order Coullet system is studied. An active control technique is applied to control this chaotic system. This type of controller is also applied to synchronize chaotic fractional-order systems in master-slave…
The inherent control switching of renewable energy sources (RESs) during intricate transient processes introduces complexity to the dynamic behavior of modern power systems. This paper reveals the dynamic coupling between grid-forming…
This paper deals with designing a robust fixed-order dynamic output feedback controller for uncertain fractional order linear time invariant (FO-LTI) systems by means of linear matrix inequalities (LMIs). Our purpose is to design a low…
The stability of dynamical systems with oscillatory behaviors and well-defined average vector fields has traditionally been studied using averaging theory. These tools have also been applied to hybrid dynamical systems, which combine…
Motivated by biochemical reaction networks, a generalization of the classical secant condition for the stability analysis of cyclic interconnected commensurate fractional-order systems is provided. The main result presents a sufficient…
We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…
In this paper we present the mathematical description and analysis of a fractional-order regulated system in the state space. A little historical background of our results in the analysis and synthesis of the fractional-order dynamical…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
In this paper, a comparative study is done on the time and frequency domain tuning strategies for fractional order (FO) PID controllers to handle higher order processes. A new fractional order template for reduced parameter modeling of…
Atangana and Baleanu proposed a new fractional derivative with non-local and no-singular Mittag-Leffler kernel to solve some problems proposed by researchers in the field of fractional calculus. This new derivative is better to describe…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…