H∞ control for a class of descriptor systems with uncertainties in the derivative matrix

This paper considers the problem of H_∞ control for descriptor systems with the derivative matrix being subjected to norm-bounded perturbations. The analysis shows that, if the problem has a solution under some assumption, the uncertainty falls only into two particular structures. For the first structure, necessary and sufficient conditions are given in terms of the so-called quadratic admissibility with H_∞ performance γ by using LMI approach. For the other structure, a sufficient condition and necessary condition are given. Numerical examples are given to illustrate the use of the results