Relative controllability of nonlinear switched fractional systems

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.