| This dissertation mainly addresses finite-time stabilization and detection problems for a class of time-varying nonlinear systems with uncertainties. For a certain class of nonlinear systems, almost disturbance attenuation and practical output tracking problem by output feedback are also investigated.; In the first part of this dissertation, we discuss some fundamental concepts and results about finite-time stability including Lyapunov theory for finite-time stability, settling time, robustness of finite-time stability, and homogeneous systems with finite time stability. Our main contribution lies in providing a systematic way to design finite-time controller for nonlinear systems and partial state finite-time controller for cascade systems. We also derive a necessary and sufficient condition for finite-tune tracking (regulation) problem. Unlike most of the existing results, our design is global rather than local and finite-time Lyapunov stability theory is applied to construct finite-time stabilizers, using the “adding a power integrator” technique.; In the second part of this dissertation, by applying an non-separation principle paradigm, we show that practical output tracking via output feedback is solvable for a class of nonlinear systems with uncertainties, for which, generally speaking, asymptotic output tracking via output feedback is impossible. For the same class of nominal nonlinear systems with bounded disturbance, the almost, disturbance attenuation problem is also solved via, output feedback. |
