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This paper is concerned with the finite-time tracking for linear and nonlinear systems, with respect to the reference signal (to be tracked by the system state) obeying some uniformity. Before the control design of finite-time tracking, an interesting and basic problem is whether or not such control exists for the system concerned. This paper aims to this basic problem. First, the sufficient and necessary conditions on finite-time tracking are proposed for linear systems. Such conditions are then extended to those for affine nonlinear systems. It should be pointed out that the sufficient and necessary conditions proposed in the paper essentially reveal the relationship between the structure of the linear/nonlinear systems and the existence of the finite-time tracking control. [ABSTRACT FROM PUBLISHER]

This paper considers the global stabilization for a class of uncertain nonlinear systems with unknown powers, unknown control directions, and unknown nonlinearities. Mainly due to the presence of the unknown powers which have not known upper bound, no existing methods are applicable to the control problem to be solved. In this paper, to compensate the serious system uncertainties and particularly to overcome the major obstruction from unknown powers, we appeal to the mechanism of switching adaptive feedback. By flexibly combining the domination and the method of adding a power integrator, we propose a new adaptive controller design, whose design parameters are tuned online based on a switching logic. The designed controller will become operative as long as finite switchings happen and will not lead to Zeno phenomenon, and can guarantee the global boundedness as well as ultimate convergence of the resulting closed-loop system. Two numerical examples are given to demonstrate the effectiveness of the developed design scheme. [ABSTRACT FROM AUTHOR]