Nonstandard Extension of H∞-Optimal Control for Singularly Perturbed Systems
In this paper, we consider a nonstandard extension of the H ∞-optimal control problem for singularly perturbed systems and relax the nonsingularity conditions made in the paper of Pan and Başar  We prove that all the results concerning the composite controller in the paper above still hold true even if the system is a nonstandard singularly perturbed system. We show that the composite optimal controller, which guarantees a disturbance attenuation level larger than the upper bound of the full-order system when ε is sufficiently small, can be constructed very simply by only revising a slow controller. This paper also provides a concise procedure to construct the composite controller. Some numerical examples, which can not be solved using the method of the above paper, are presented to illustrate the theoretical results.
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