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In this paper, a necessary and sufficient condition for generalized quadratic stabilization of switched descriptor time‐delay (SDT) systems under arbitrary switching is investigated. Based on the linear matrix inequality (LMI) method, some results are given: (i) the SDT system is regular, impulse‐free, and stable under arbitrary switching; (ii) the necessary and sufficient condition for switched generalized quadratic stability (stabilization) of the uncertain SDT systems is derived. Finally, a numerical example is provided to illustrate the effectiveness of the method.

Abstract. In this paper, necessary and sufficient conditions are given for the existence of the group inverse of the block matrix A A B 0 ¡ over any skew field, where A, B are both square and rank(B) ≥ rank(A). The representation of this group inverse and some relative additive results are also given.

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