Abstract
Abstract This paper derives results for the stabilizing and synchronizing controller for a generalized class of nonlinear systems connected in chain configuration. The proposed procedure utilizes contraction based backstepping approach blended with Gershgorin theorem instead of Lyapunov stability based backstepping technique for designing controllers for such systems. A systematic step by step strategy is adopted to obtain a single controller to achieve stabilization of states of systems. Further, results are extended to synchronize the systems belonging to the given generalized class of nonlinear systems. The proposed procedure leads to quite a simple controller for targeted synchronization task in comparison to existing controllers in literature for such class of systems. The systems among which the synchronization has to be done are assumed to be connected in chain formation through one-way coupling. To verify the efficacy of the proposed approach, chaotic systems such as Lorenz-Stenflo, Chen, L u ¨ and Lorenz systems have been considered and detailed numerical validations are presented appropriately.
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