Abstract
Contractive nonlinear systems possess numerous desirable properties, which have drawn considerable attention from the control community. The work proposes an extended HGO based output feedback strategy, which can assure contraction of a class of uncertain singularly perturbed (SP) systems. The analysis differs from the conventional Lyapunov approach in two aspects: the convergence bounds explicitly depend on the singular perturbation parameter (SPP); and the sufficient conditions for contraction do not require any interconnection conditions. Moreover, it is observed that the requirement of the smallness of SPP can be relaxed for certain classes of nonlinear systems. The derived bounds also reveal a particular trade-off between the contraction rates and condition numbers associated with the transformation metric. These bounds offer additional degree of freedom in tuning the closed loop performances apart from reducing the SPP. Multiple numerical simulations point to the veracity of the claims.
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