In this paper, we propose a control system design to satisfy multiconstraints in the time and frequency domains using the framework of continuous time deadbeat control. At first, two conditions are introduced for the free parameter of
H∞ suboptimal controllers corresponding to an interpolation condition for the deadbeat control and a norm constraint for the
H∞, control. The parametrization of the controllers satisfying the two conditions simultaneously is given by restricting the modified free parameters of
H∞, controllers to commensurate time delay functions. The other constraints of approximated
L1 norm or
L2 norm are also reduced to convex finite-dimensional problems and these mixed problems are solved numerically.
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