Prescribed-Time Control for Linear Systems in Canonical Form via Nonlinear Feedback

For systems in canonical form with nonvanishing uncertainties/disturbances, this work presents an approach to full-state regulation within prescribed time irrespective of initial conditions. By introducing the smooth hyperbolic-tangent-like function, a nonlinear and time-varying state-feedback control scheme is constructed, which is further extended to address output-feedback-based prescribed-time regulation by invoking the prescribed-time observer, all are applicable over the entire operational time zone. As an alternative to full-state regulation within the user-assignable time interval, the proposed method analytically bridges the divide between linear and nonlinear feedback-based prescribed-time control and is able to achieve asymptotic stability, exponential stability, and prescribed-time stability with a unified control structure.