Finite-time integral control for a class of nonlinear planar systems with non-vanishing uncertainties

This paper considers the problem of globally regulating a class of planar nonlinear systems perturbed by various non-vanishing uncertainties including constant step disturbances, exogenous time-varying disturbances with unknown magnitudes, and modeling uncertainties with unknown system parameters. A new integral controller consisting of a nonlinear integral dynamic and a semi-linear control law is constructed to drive the states of the uncertain systems to the origin in a finite time. This is achieved by three major mechanisms: (i) for the purpose of finite-time convergence, a lower-order integral dynamic is first constructed; (ii) by revamping the technique of adding a power integrator, a semi-linear control law containing a linear corrective term is proposed to handle the various forms of uncertainties; and (iii) a new inequality is established to provide an effective estimating tool for the selection of a suitable control gain to guarantee finite-time stability.