The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach.

The book is intended to make available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.

Discrete-time systems arise as a matter of course in modelling biological or economic processes. For systems and control theory they are of major importance, particularly in connection with digital control applications. If sampling is performed in order to control periodic processes, almost periodic systems are obtained. This is a strong motivation to investigate the discrete-time systems with time-varying coefficients. This research monograph contains a study of discrete-time nodes, the discrete counterpart of the theory elaborated by Bart, Gohberg and Kaashoek for the continuous case, discrete-time Lyapunov and Riccati equations, discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators. All these tools aim to solve the problems of stabilization and attenuation of disturbances in the framework of H2- and H-control theory. The book is the first of its kind to be devoted to these topics and consists mainly of original, recently obtained results.

Discrete-time systems arise as a matter of course in modelling biological or economic processes. For systems and control theory they are of major importance, particularly in connection with digital control applications. If sampling is performed in order to control periodic processes, almost periodic systems are obtained. This is a strong motivation to investigate the discrete-time systems with time-varying coefficients. This research monograph contains a study of discrete-time nodes, the discrete counterpart of the theory elaborated by Bart, Gohberg and Kaashoek for the continuous case, discrete-time Lyapunov and Riccati equations, discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators. All these tools aim to solve the problems of stabilization and attenuation of disturbances in the framework of H2- and H-control theory. The book is the first of its kind to be devoted to these topics and consists mainly of original, recently obtained results.

OO It is a matter of general consensus that in the last decade the H _ optimization for robust control has dominated the research effort in control systems theory. Much attention has been paid equally to the mathematical instrumentation and the computational aspects. There are several excellent monographs that cover the standard topics in the area. Among the recent issues we have to cite here Linear Robust Control authored by Green and Limebeer (Prentice Hall 1995), Robust Controller Design Using Normalized Coprime Factor Plant Descriptions - by McFarlane and Glover (Springer Verlag 1989), Robust and Optimal Control - by Zhou, Doyle and Glover (Prentice Hall 1996). Thus, when the authors of the present monograph decided to start the work they were confronted with a very rich literature on the subject. However two reasons motivated their initiative. The first concerns the theory in which the whole development of the book was embedded. As is well known, there are several ways of approach oo ing H and robust control theory. Here we mention three relevant direc tions chronologically ordered: a) the first makes use of a generalization of the Beurling-Lax theorem to Krein spaces; b) the second makes use of a generalization of Nevanlinna-Pick interpolation theory and commutant lifting theorem; c) the third, and probably the most attractive from an el evate engineering viewpoint, is the two Riccati equations based approach which offers a complete solution in state space form."

The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach.

The book is intended to make available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.

Seven writings assembled in the context of the philosophy of art that Jean-Francois Lyotard developed in the 1980s, at the time of the Differend (1983) and of the "Kantian turn" leading to the Lessons on the Analytic of the Sublime (1992), are here published for the first time in English translation. The texts focus on three artists with widely divergent aesthetic orientations: the colorist-draftsman Valerio Adami, the conceptual metaphysician Shusaku Arakawa, and Daniel Buren, the "pragmatist of the invisible."

These three protagonists share the notion that the interest in art does not lie in the simple denotation of a frame of reference, but in the connotations of material nuances, in flavors, in tones in one word, the visual, that is barely revealed in the anamnesis that guides the visible and provokes the essential inquietude of the aesthetic experience. What to Paint? Not reality or a world, nor a rich subjectivity, nor even the phantasms of dreams or ideals of being-together, but the act of painting itself, and, beyond the performance of the painter, the presence of matters, a presence that in Arakawa's word is quite obviously blank, elusive."