PrefaceControl system analysis and design are important fields in the engineering sciences. Process identification and optimum design have developed rapidly over the past decades and resulted in great engineering progress. However, many results have suffered from considerable dependence on uncertainties, mainly incorporated in the plant, in actuators and sensors, and released by other internal disturbances.More and more, methods tackling uncertainties form a central and important issue in designing feedback control systems. Choosing appropriate design methods, the influence of uncertainties on the closed-loop behaviour can be reduced to a large extent. Control systems particularly designed to manage uncertainties are called robust control systems. Robust control theory provides a design philosophy with respect to perturbed or uncertain parts of the system. This monograph is devoted to plants and their approximate models and to the discussion of their uncertainties. The thrust of the book is on systematic representation of methods for robust control.Most of the important areas of robust control are covered. The aim is to provide an introduction to the theory and methods of robust control system design, to present a coherent body of knowledge, to clarify and unify presentation, and to streamline derivations and proofs in the field of uncertainties and robust control. The book contains a thorough treatment of important material which is scattered throughout the literature.The primary goal of the text is to present significant derivations and proofs. As far as less significant proofs or lengthy derivations are concerned, only the results are outlined and the reader is referred to the literature relevant to this subject. In a few cases, some topics are set forth only as a suggestion for further reading.Some important problems treated in this book are:• How is uncertainty described and bounded when applying methods of differential equations, transfer functions or transfer matrices, state-space algorithms or some approximating calculus?• Which uncertainty or which perturbation in some special system description forces the system to instability? This question arises both for open-loop and for closed-loop systems.• Which kind of controller is able to tolerate maximum uncertainty?2In most cases stability robustness is applied but performance robustness is also a very important subject, e.g., determining the regions in the parameter space of controllers which place all the closed-loop eigenvalues into a desired region, thus satisfying the design specifications in the face of uncertain but bounded plant parameters.The book is intended specifically for practicing but mathematically inclined engineers, for postgraduate students and engineers on master's level. Moreover, the book is intended for those readers who wish to apply robust design principles and theories to real-life applications and problems.Emphasis is put on practical considerations and on applicability at the expense of extensive proofs and mathematical rigor.The ...

Asymptotic expansions of certain generalized Bernoulli polynomials are obtained, some in terms of elementary functions and others in terms of gamma functions and their derivatives. The latter results can also be written in terms of elementary functions, by using the known asymptotic expansions of the gamma functions, and the leading terms are obtained in this way. The results obtained give the asymptotic form of the coefficients occurring in all the usual central-difference formulae of the calculus of finite differences.

Gradients and matricial gradients for optimally increasing the stability margin and the admissible uncertainty of a dynamic system are the targets of this presented article. To design a dynamic system, the gradients are used in a dialog between a system scientist and gradient-based computer support. The stability margin is derived for output state controllers, including regular state controllers. The resonant frequency and the damping factors are investigated as a direct function of the maximum admissible uncertainty. The resulting gradients are extended to observer-assisted controllers, to minimum-order observers, and to dynamic-output state controllers.

A trade-off between optimum allocation of the entire set of eigenvalues and the size of controller norm or a general actuator effort is carried out for continuous-time and discrete-time systems. Controllers achieving appropriate results are termed holistic. The design is based on the trace and determinant of the closed-loop state-space matrix. To solve the problem within the scope of actuating effort, the norm of the state controller matrix or the actuator effort transfer matrix are taken into consideration. The method is also extended for designing holistic observers. For preserving stability, a Lyapunov condition is included.Keywords: trace of the inverse, multivariable continuous-time and discrete-time controllers and observers; Lyapunov condition; constraint on actuator effort Regelsystementwurf auf der Basis holistischer Eigenwertvorgabe. Die Vorgabe derEigenwerte einer linearen Mehrgr6genregelung wird in ihrer Gesamtheit besorgt. Regler, die diese Vorgabe erfª werden als holistisch bezeichnet. Der Entwurf benutzt nur die Spur der inversen Koeffizientenmatrix der geschlossenen Regelung bzw. die Determinante der Koeffizientenmatrix direkt bei kontinuierlichen bzw. zeitdiskreten Systemen. Obwohl diese Methode von einer nur notwendigen Stabilit~itsbedingung ausgeht, ist sie auch auf instabile Regelstrecken anwendbar. Als Rahmen fª die holistische Eigenwertvorgabe ist nur ein Richtwert des Steueraufwands erfordehich, mit dem sie optimal in Abstimmung gebracht wird. Die Methode ist auch auf holistische Beobachter ausgedehnt und um eine Lyapunov-Bedingung fª Stabilit~it erweitert. SchlªSpur der inversen Koeffizientenmatrix des Regelkreises; Determinante der Koeffizientenmatrix; kontinuierliche und zeitdiskrete Mehrgr6gensysteme; holistischer Mehrgr6genregler und -beobachter; Lyapunov-Nebenbedingung; Rahmenbeschr~inkung des Stellaufwands

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