Stabilization of Uncertain Singularly Perturbed Systems With Pole-Placement Constraints

This brief considers the problem of stabilization of uncertain singularly perturbed systems with pole-placement constraints by using
$H^infty$
dynamic output feedback design. Based on the Lyapunov stability theorem and the tool of linear matrix inequality (LMI), we solve dynamic output feedback gain matrices and a set of common positive-definite matrices, and then some sufficient conditions are derived to stabilize the singularly perturbed systems with parametric uncertainties. Moreover, the developed
$H^infty$
criterion guarantees that the influence of external disturbance is as small as possible and the poles of the closed-loop system are all located inside the LMI stability region. By the guaranteed
$varepsilon$
-bound issue, the proposed scheme can stabilize the systems for all
$varepsilonin(0,varepsilon^ast)$
. A circuit system is given to illustrate the validity of the proposed schemes.