Prescribed-Time Observers for Linear Systems in Observer Canonical Form

For linear systems in the observer canonical form, we introduce a state observer with time-varying gains that tend to infinity as time approaches a prescribed convergence time. The observer is shown to exhibit fixed-time stability with an arbitrary convergence time, which is prescribed by the user irrespective of initial conditions. The output estimation error injection terms are also shown to remain uniformly bounded and converge to zero at the prescribed time.