Affiliation:
1. School of Mathematical Sciences, Anhui University Hefei China
2. The Center for Pure Mathematics Anhui University Hefei China
3. School of Mathematics Hefei University of Technology Hefei China
Abstract
AbstractThis article investigates relative controllability of nonlinear switched fractional systems (SFSs). With the aid of Mittag‐Leffler functions and invariant subspace theory, two sufficient and necessary conditions for corresponding linear SFSs are first established. Then, piecewise continuous control functions and a novel nonlinear operator are constructed to overcome the difficulties arising from switching rules, nonlinearity, and fractional derivatives. Under different constraints on nonlinear functions, two controllability conditions depending on system parameters for nonlinear SFSs are proposed by applying Schauder's and Banach's fixed point theorems, respectively. The obtained criteria may well show the influence of coefficient matrices, fractional derivatives, and switching rules on relative controllability. In addition, our proposed method is also applicable for integer‐order switched systems. Finally, two simulated examples are worked out to verify the theoretical results.
Funder
National Natural Science Foundation of China
Subject
Control and Systems Engineering,Electrical and Electronic Engineering,Mathematics (miscellaneous)