Homogeneous in the Bi-Limit Output Feedback Control for a Class of SISO LTV Systems

In this article, we construct an output feedback control scheme tailored to a class of linear time-varying (LTV) systems with a single output and single matched non-vanishing perturbation. The control is shown to be capable of stabilizing the origin of the system in finite-time, or even more, in fixed-time. The result is obtained by constructing a nonlinear homogeneous in the bi-limit controller and observer. For a particular choice of parameters and gains, a high-order sliding mode (HOSM) controller is obtained, capable of global convergence when the system perturbation is bounded. The closed-loop stability of the system is demonstrated by means of a bl-homogeneous Lyapunov function, which allows us to conclude a principle of separation between the observer and controller design. The effectiveness of the proposal is illustrated by an academic example.