Observer-based Prescribed Finite-time Control for Singularly Perturbed Systems

This article investigates finite-time output feedback control for singularly perturbed systems with unmeasurable states. Such systems feature dynamics operating on two distinct time scales, increasing complexity due to coupled subsystems and state constraints. First, an observer-based composite controller is designed separately for slow and fast subsystems. Next, using solutions from parametric Lyapunov equations, an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\varepsilon$</tex>-dependent Lyapunov function is constructed to determine suitable time-varying control gains. Both the state feedback and observer gains vary over time, ensuring finite-time stability of the closed-loop system. Finally, the proposed strategy is validated through an example of an armature control system.