Abstract
This paper studies the finite-time stability of fractional singular time-delay systems. First, by the method of the steps, we discuss the existence and uniqueness of the solutions for the equivalent systems to the fractional singular time-delay systems. Furthermore, we give the Mittag-Leffler estimation of the solutions for the equivalent systems and obtain the sufficient conditions of the finite-time stability for the original systems.
Highlights
In the past years or so, fractional calculus has attracted many physicists, mathematicians, and engineers, and notable contributions have been made to both the theory and the applications of fractional differential equations
The different techniques have been applied to investigate the stability of various fractional dynamical systems, such as the principle of contraction mappings [ ], the Lyapunov direct method [ ], linear matrix inequalities [ ], Gronwall inequalities [ – ] and fixed-point theorems [ ]
We notice that large numbers of practical systems, such as economic systems, power systems and so on, are singular differential systems which are named differential-algebraic systems or descriptor systems
Summary
In the past years or so, fractional calculus has attracted many physicists, mathematicians, and engineers, and notable contributions have been made to both the theory and the applications of fractional differential equations (see [ – ]). In [ – ], the authors discuss singular systems with or without delay and obtain some important results. We consider the following fractional singular time-delay system: E(cDαx(t)) = Ax(t) + Bx(t – τ ), t ∈ [ , T],
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