Abstract
This brief considers the problem of stabilization of uncertain singularly perturbed systems with pole-placement constraints by using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H^infty$</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H^infty$</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$varepsilon$</tex> -bound issue, the proposed scheme can stabilize the systems for all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$varepsilonin(0,varepsilon^ast)$</tex> . A circuit system is given to illustrate the validity of the proposed schemes.
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