2016/05/31 by Vincent Andrieu, Andrieu, Vincent, Bayu Jayawardhana +3
Computer Science · Engineering · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1605.09679
openalex publication_date 2016/05/31 · openalex created_date 2017/06/15 · openalex updated_date 2026/07/28
Based on recent works on transverse exponential stability, we establish some necessary and sufficient conditions for the existence of a (locally) exponential synchronizing control law. We show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems (on the synchronization manifold) by a linear state feedback. This, in turn, is also equivalent to the existence of a symmetric covariant tensor field, which satisfies a Control Matrix Function inequality. Based on this result, we provide the construction of such synchronizer via backstepping approaches. In some particular cases, we show how global exponential synchronization may be obtained.