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Convergence Time Bounds for a Family of Second-Order Homogeneous State-Feedback Controllers

This letter studies a family of second-order homogeneous state-feedback controllers, which includes the well-known twisting algorithm as a special case. Upper bounds for the closed loop’s convergence time are proposed that may be computed analytically for any values of the positive controller parameters. Numerical comparisons show that the bound approximates the actual convergence time to within a factor of two over a large parameter range.