Roger C. E. Tan

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In this paper, algebraic characterizations for the positive realness of descriptor systems are studied. It is shown that the positive realness of descriptor systems can be determined by solving a linear matrix inequality, and hence the celebrated positive real lemma for standard state space systems is extended to descriptor systems. In addition, the(More)
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the(More)
1Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore 2Institute of Mathematical Science, Fudan University, Shanghai, 200433, People’s Republic of China 3School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China 4Shanghai Key Laboratory of Contemporary Applied(More)