Singularly perturbed implicit control law for linear time varying SISO system. Part II: State observation

This paper considers the problem of stabilizing a single-input single-output linear time varying system using a low order controller and an equalizer filter. The closed loop is a linear singularly perturbed system with uniform asymptotic stability behavior. Following the results of Kokotović's book, we show how to design a control scheme, control law plus state observer, such that the system dynamics is assigned by a Hurwitz polynomial with constant coefficients. We calculate bounds, ε ∈ (0, ε*), for guaranteeing the uniform asymptotic stability of the singularly perturbed closed loop system.