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If one takes the intuitive point of view that a system is a black box whose inputs and outputs are time functions or time series it is natural to adopt an operator theoretic approach to the stUdy of such systems. Here the black box is modeled by an operator which maps an input time function into an output time function. Such an approach yields a unification of the continuous (time function) and discrete (time series) theories and simultaneously allows one to formulate a single theory which is valid for time-variable distributed and nonlinear systems. Surprisingly, however, the great potential for such an approach has only recently been realized. Early attempts to apply classical operator theory typically having failed when optimal controllers proved to be non-causal, feedback systems unstable or coupling networks non-lossless. Moreover, attempts to circumvent these difficulties by adding causality or stability constraints to the problems failed when it was realized that these time based concepts were undefined and; in fact, undefinable; in the Hilbert and Banach spaces of classical operator theory.
This book was the first and remains the only book to give a comprehensive treatment of the behavior of linear or nonlinear systems when they are connected in a closed-loop fashion, with the output of one system forming the input of the other. The study of the stability of such systems requires one to draw upon several branches of mathematics but most notably functional analysis. Feedback Systems: Input-Output Properties includes the most basic concepts of matrices and norms, the important fundamental theorems in input-output stability, and the requisite background material in advanced topics such as the small gain theorem and the passivity theorem. Audience: advanced graduate students and researchers in control theory, dynamical systems, and ordinary and partial differential equations.
The objective of this conference was to foster a healthy exchange of ideas and experience in the domain of multiple criteria problem solving. This conference was an outgrowth of an earlier conference I organized with Herve Thiriez at CESA, Jouy-en-Josas, France in 1975 during my stay at the European Institute in Brussels. When I re joined the State University of New York at Buffalo that year, I be gan to search for potential sponsors for this conference. Approxi mately one year later when the prospects began to look promising, I contacted several individuals to act as an informal coordinating committee for the conference. I wanted to avoid biasing the con ference completely to my way of thinking! The members of this committee were Jim Dyer, Peter Fishburn, Ralph Kee. ney, Bernard Roy (Universite de Paris IX Dauphine who was unable to participate in the conference), and Milan Zeleny. Though the committee did not meet, per se, their inputs regarding format, possible participants, number of participants, length of the conference, and so on were of great value to me in planning and organizing the conference. I wish to acknowledge the contributions of this group. We were most fortunate in obtaining the financial support of the European Institute for Advanced Studies in Management, Brussels ยท(one of the sponsors of the Jouy-en-Josas conference), the Office of Naval Research, and the State University of New York at Buffalo.