Abstract
The consensus problem for a class of fractional-order nonlinear multiagent systems with a distributed protocol containing input time delay is investigated in this paper. Consider both cases of constant time delay and time-varying delay, the delay-independent consensus conditions are obtained to achieve the consensus of the systems, respectively, by adopting the linear matrix inequality (LMI) methods and stability theory of fractional-order systems. As illustrated by the numerical examples, the proposed theoretical results work well and accurately.
Highlights
Fractional Calculus. e Riemann–Liouville and the Caputo fractional-order derivatives are two commonly used definitions. e autonomous fractional-order systems modeled with Caputo derivative could be converted to the similar initial value problem (IVP) and could have definite physical meaning
In order to realize the leader-following consensus of systems (5)-(6), we propose the following distributed control protocol with time delay: N
For any initial condition. e aim of this paper is to discuss the feasible consensus conditions to the system. e measurement error between agent i and the leader is defined as εi(t) xi(t) − x0(t); multiagent systems (5)-(6) controlled by (7) can be rewritten as
Summary
Some preliminary knowledge about the concepts of algebraic graph theory and fractional calculus are introduced. A directed graph contains a directed spanning tree if there exists a leader node 0, such that it has directed paths to all other following nodes in G. E Riemann–Liouville and the Caputo fractional-order derivatives are two commonly used definitions. E autonomous fractional-order systems modeled with Caputo derivative could be converted to the similar initial value problem (IVP) and could have definite physical meaning. We will use the fractionalorder derivative with Caputo definition in this paper. The definition of fractional-order integral [33] is. As the Caputo fractional-order derivative β is close to 1, the property limβ⟶1− [C0 Dβt f(t)] f_(t) holds if f(t) is differentiable [32].
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