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H-infinity Control for Nonlinear Descriptor Systems
The authors present a study of the H-infinity control problem and related topics for descriptor systems, described by a set of nonlinear differential-algebraic equations. They derive necessary and sufficient conditions for the existence of a controller solving the standard nonlinear H-infinity control problem considering both state and output feedback. One such condition for the output feedback control problem to be solvable is obtained in terms of Hamilton–Jacobi inequalities and a weak coupling condition; a parameterization of output feedback controllers solving the problem is also provided. All of these results are then specialized to the linear case. The derivation of state-space formulae for all controllers solving the standard H-infinity control problem for descriptor systems is proposed. Among other important topics covered are balanced realization, reduced-order controller design and mixed H2/H-infinity control. "H-infinity Control for Nonlinear Descriptor Systems" provides a comprehensive introduction and easy access to advanced topics.
New Approaches in Spectral Decomposition
Aimed at a general mathematical audience, this book provides a careful exposition of developments in the theory of spectral decomposition. Bringing the reader from the basics up to the level of current research in the area at the time of writing, Lange and Wang present an accessible account of the techniques used in the theory and applications of decomposable operators and related classes of operators. The book begins with a discussion of criteria for decomposable and related types of operators, and an analysis that relates and distinguishes among them. Perturbation theory of decomposable and other operators, applications to classical Hilberty space operators, quasisimilarity, and a new class of weakly decomposable operators are also discussed. The book closes with an exposition of some classical theories on invariant subspaces for subdecomposable and hyponormal operators, and a presentation of the parallel spectral theory of commuting systems.
A Local Spectral Theory for Closed Operators
This book, which is almost entirely devoted to unbounded operators, gives a unified treatment of the contemporary local spectral theory for unbounded closed operators on a complex Banach space. While the main part of the book is original, necessary background materials provided. There are some completely new topics treated, such as the complete spectral duality theory with the first comprehensive proof of the predual theorem, in two different versions. Also covered are spectral resolvents of various kinds (monotomic, strongly monotonic, almost localized, analytically invariant), and spectral decompositions with respect to the identity. The book concludes with an extensive reference list, including many papers published in the People's Republic of China, here brought to the attention of Western mathematicians for the first time. Pure mathematicians, especially those working in operator theory and functional analysis, will find this book of interest.
Functional Analysis in China
Functional Analysis has become one of the main branches in Chinese mathematics. Many outstanding contributions and results have been achieved over the past sixty years. This authoritative collection is complementary to Western studies in this field, and seeks to summarise and introduce the historical progress of the development of Functional Analysis in China from the 1940s to the present. A broad range of topics is covered, such as nonlinear functional analysis, linear operator theory, theory of operator algebras, applications including the solvability of some partial differential equations, and special spaces that contain Banach spaces and topological vector spaces. Some of these papers have made a significant impact on the mathematical community worldwide. Audience: This volume will be of interest to mathematicians, physicists and engineers at postgraduate level.
Healing Energy
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Asian Folk Religion and Cultural Interaction
This book uses a cultural interaction approach to discuss numerous temples and shrines of Sinitic origin that house Daoist, Buddhist, and folk gods. Such deities were transmitted outside the Chinese continent, or were introduced from other regions and syncretized. Examples include temple guardian gods that arrived in Japan from China and later became deified as part of the Five Mountain system, and a Daoist deity that transformed into a god in Japan after syncretizing with My?ken Bosatsu. The profoundly different images of Ksitigarbha in China and Japan are discussed, as well as Mt. Jiuhua, the center of Ksitigarbha in modern China. Lastly, the process by which Sinitic gods were transmitted to regions outside of the Chinese continent, such as Taiwan, Singapore, and Okinawa, is explored.
