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Small-Time Local Controllability of Switched Nonlinear Systems

This article considers the small-time local controllability (STLC) of switched nonlinear systems (SNSs). First, the original SNS is associated with a nilpotent Lie algebra, on which the solutions of the SNS are approximated by the hybrid Lie power series. Second, the concepts of high-order control variations and bad Lie brackets are defined for SNSs from a geometrical point of view. This helps to establish a new high-order sufficient STLC condition that is closely related to “neutralized” bad Lie brackets. Finally, it is shown that the obtained general condition is compatible with the existing controllability conditions of switched linear systems and nonswitched linear and nonlinear systems.