Back‐stepping stabilization of fractional‐order triangular system with applications to chaotic systems

Abstract

AbstractThis paper addresses the stabilization of fractional‐order nonlinear lower triangular systems and applies the obtained results to the synchronization of fractional‐order chaotic systems (FOCSs). Three cases are considered as follows: (i) FOCSs have a lower triangular structure themselves. (ii) FOCSs can be converted into the form in full by appropriate nonsingular coordinate transformations. (iii) FOCSs can be transformed into the structure in part by the conversions. It is shown that the above three cases combining with back‐stepping approach are useful for the control of FOCSs. Different from the previous literature, the system structure studied is more concise with more applications. A numerical example is presented to show the validity of the proposed results.