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This paper proposes a new direct approach to control the transient response of a LTI system. The characteristic of a repeated-pole system is first studied. It can be shown that the step response of this kind of system has no overshoot. µ-scaled characteristic ratios, β i = µα i , i =1, n, and τ are introduced, where α i is the principal characteristic ratio and τ is the generalized time constant. It is shown that two parameters, µ and τ, are used to successfully control the overshoot and the transient time of all minimum phase LTI systems. The result shows that the proposed method is comparable to the method proposed by Bhattacharyya [1], but more luminous and simple in approach.

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The problems of prediction, ® ltering, smoothing and deconvolution are formulated and solved for a discrete time linear system in an H ¥ setting over a ® nite interval. The measurement noise and process noise have bounded energies. The case with known initial conditions is considered. The approach uses a basic quadratic game theory in a discrete time-domain H ¥ setting.