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This paper examines the problem of the control of multivariable linear time-invariant dynamical systems with bounded controllers using the Variable Structure Control (VSC) approach. New type of Lyapunov functions is introduced. The domain of attraction for this class of systems is obtained. A coordinate transformation for decoupling the "fast" and "slow" states is also presented. This transformation can also be used in the investigation of variable structure and high gain feedback systems. A pole placement problem in high gain feedback conrol systems is then considered and illustrated by means of a numerical example.