Singularly perturbed implicit control law for linear time varying SISO system

This paper considers the problem of stabilizing a single input-single output linear time varying system using a low order controller and equalizer filter. The closed loop system is a linear singularly perturbed system with uniform asymptotic stability behavior; we calculate bounds ε ∈ (0, ε*) as in, such that the uniform asymptotic stability of the singularly perturbed system is guaranteed. Following the results of we show how to design a control law such that the system dynamics is assigned by a Hurwitz polynomial with constant coefficients.