Download or read book Properties of Time varying Linear Systems written by Allen Gersho and published by . This book was released on 1961 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: A time-frequency duality is used to lead to a more complete characterization of time-varying linear systems. Several system functions are defined, which may be used to relate the input and output signals in different ways. In particular, a new transfer function is introduced that is dual to Zadeh's H transfer function for time-varying systems. The use of this transfer function leads to a new class of separable models for synthesizing time-varying systems. It is shown that under appropriate conditions either transfer function is determined uniquely from its real part. A new synthesis procedure based on the real-part sufficiency of the transfer function is described. (Author).

Download or read book Linear Time Varying Systems written by Henri Bourlès and published by Springer. This book was released on 2011-04-21 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to propose a new approach to analysis and control of linear time-varying systems. These systems are defined in an intrinsic way, i.e., not by a particular representation (e.g., a transfer matrix or a state-space form) but as they are actually. The system equations, derived, e.g., from the laws of physics, are gathered to form an intrinsic mathematical object, namely a finitely presented module over a ring of operators. This is strongly connected with the engineering point of view, according to which a system is not a specific set of equations but an object of the material world which can be described by equivalent sets of equations. This viewpoint makes it possible to formulate and solve efficiently several key problems of the theory of control in the case of linear time-varying systems. The solutions are based on algebraic analysis. This book, written for engineers, is also useful for mathematicians since it shows how algebraic analysis can be applied to solve engineering problems. Henri Bourlès is a Professor and holds the industrial automation chair at the Conservatoire national des arts et métiers in France. He has been teaching automation for over 20 years in engineering and graduate schools. Bogdan Marinescu is currently research engineer at the French Transmission System Operator (RTE) and Associate Professor at SATIE-Ecole Normale Supérieure de Cachan.

Download or read book Analysis of Periodically Time Varying Systems written by John A. Richards and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of the practical techniques developed for treating systems described by periodic differential equations have arisen in different fields of application; con sequently some procedures have not always been known to workers in areas that might benefit substantially from them. Furthermore, recent analytical methods are computationally based so that it now seems an opportune time for an applications-oriented book to be made available that, in a sense, bridges the fields in which equations with periodic coefficients arise and which draws together analytical methods that are implemented readily. This book seeks to ftll that role, from a user's and not a theoretician's view. The complexities of periodic systems often demand a computational approach. Matrix treatments therefore are emphasized here although algebraic methods have been included where they are useful in their own right or where they establish properties that can be exploited by the matrix approach. The matrix development given calls upon the nomenclature and treatment of H. D'Angelo, Linear Time Varying Systems: Analysis and Synthesis (Boston: Allyn and Bacon 1970) which deals with time-varying systems in general. It is recommended for its modernity and comprehensive approach to systems analysis by matrix methods. Since the present work is applications-oriented no attempt has been made to be complete theoretically by way of presenting all proofs, existence theorems and so on. These can be found in D'Angelo and classic and well-developed treatises such as McLachlan, N. W. : Theory and application of Mathieu functions.

Download or read book Characterization of Time varying Linear Systems written by Allen Gersho and published by . This book was released on 1963 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that a versatile description of time-varying linear systems is achieved by the use of a family of eight system functions that includes the G and H transfer functions. This approach is extended to multidimensional systems and to ''vector-time'' systems operating on signals that are specified by a function of several variables. The class of time-varying linear systems that is specified implicitly by a set of nth order linear differential equations in r variables is considered. The explicit form of the impulse response of the system is derived in order to bridge the gap between the differential equation and the system-function specifications of a time-varying linear system. The same basic approach for characterizing deterministic systems leads to procedures for the characterization of randomly varying systems subjected to random inputs. The general case where the system and input are nonstationary is considered for both unidimensional and multidimensional systems. (Author).

Download or read book Linear Time varying Approximations to Nonlinear Dynamical Systems written by Maria Tomas-Rodriguez and published by Springer Science & Business Media. This book was released on 2010-02-04 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those – well-known – based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.

Download or read book Linear Time varying Systems written by Kostas S. Tsakalis and published by . This book was released on 1993 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Characterization of Discrete time Linear Periodically Time varying Systems written by Kevin W. Baugh and published by . This book was released on 1991 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Parameter Varying and Time Delay Systems written by Corentin Briat and published by Springer. This book was released on 2014-09-03 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the analysis and control of Linear Parameter-Varying Systems and Time-Delay Systems and their interactions. The purpose is to give the readers some fundamental theoretical background on these topics and to give more insights on the possible applications of these theories. This self-contained monograph is written in an accessible way for readers ranging from undergraduate/PhD students to engineers and researchers willing to know more about the fields of time-delay systems, parameter-varying systems, robust analysis, robust control, gain-scheduling techniques in the LPV fashion and LMI based approaches. The only prerequisites are basic knowledge in linear algebra, ordinary differential equations and (linear) dynamical systems. Most of the results are proved unless the proof is too complex or not necessary for a good understanding of the results. In the latter cases, suitable references are systematically provided. The first part pertains on the representation, analysis and control of LPV systems along with a reminder on robust analysis and control techniques. The second part is concerned with the representation and analysis of time-delay systems using various time-domain techniques. The third and last part is devoted to the representation, analysis, observation, filtering and control of LPV time-delay systems. The book also presents many important basic and advanced results on the manipulation of LMIs.

Download or read book Time Varying Discrete Linear Systems written by Aristide Halanay and published by Birkhäuser. This book was released on 2012-12-06 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Analysis and Control of Linear Time Varying Systems written by Henri Bourles and published by Iste Press - Elsevier. This book was released on 2020-11 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of the book is the study of structural properties of linear time-varying systems (in particular, controllability, observability, and stability) using algebraic analysis, and the control of these systems (including reference tracking and disturbance rejection).

Download or read book Time Varying Systems and Computations written by Patrick DeWilde and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex function theory and linear algebra provide much of the basic mathematics needed by engineers engaged in numerical computations, signal processing or control. The transfer function of a linear time invariant system is a function of the complex vari able s or z and it is analytic in a large part of the complex plane. Many important prop erties of the system for which it is a transfer function are related to its analytic prop erties. On the other hand, engineers often encounter small and large matrices which describe (linear) maps between physically important quantities. In both cases similar mathematical and computational problems occur: operators, be they transfer functions or matrices, have to be simplified, approximated, decomposed and realized. Each field has developed theory and techniques to solve the main common problems encountered. Yet, there is a large, mysterious gap between complex function theory and numerical linear algebra. For example, complex function theory has solved the problem to find analytic functions of minimal complexity and minimal supremum norm that approxi e. g. , as optimal mate given values at strategic points in the complex plane. They serve approximants for a desired behavior of a system to be designed. No similar approxi mation theory for matrices existed until recently, except for the case where the matrix is (very) close to singular.

Download or read book Analysis of Randomly Time varying Linear Systems written by Arnold Rosenbloom and published by . This book was released on 1954 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Analytical Techniques for Linear Time varying Systems written by Nathan Arthur Liskov and published by . This book was released on 1965 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definition of several new system functions leads to a more complete characterization of time-varying linear systems. A family of twelve system functions, including the impulse-response K system functions, are used to describe time-varying linear systems. The relationships among the various system functions are clearly illustrated. The K system functions are shown to be convenient for the analysis of cascaded systems. The time-frequency duality concept is discussed with respect to the system functions, and the introduction of physical variables extends the duality concept so that knowing one relationship is equivalent to knowing four relationships. The expansion of system functions in terms of a complete set of functions in two dimensional space or in a sampling series for an appropriately band-limited and/or time- limited system leads to a matrix characterization of time-varying linear systems. Schemes for evaluating the coefficients of the expansions are described.

Download or read book Signals and Transforms in Linear Systems Analysis written by Wasyl Wasylkiwskyj and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7. The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to serve as a text on signals and transforms for a first year one semester graduate course, primarily for electrical engineers.

Download or read book Sensitivity Analysis in Linear Systems written by Assem Deif and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text surveying perturbation techniques and sensitivity analysis of linear systems is an ambitious undertaking, considering the lack of basic comprehensive texts on the subject. A wide-ranging and global coverage of the topic is as yet missing, despite the existence of numerous monographs dealing with specific topics but generally of use to only a narrow category of people. In fact, most works approach this subject from the numerical analysis point of view. Indeed, researchers in this field have been most concerned with this topic, although engineers and scholars in all fields may find it equally interesting. One can state, without great exaggeration, that a great deal of engineering work is devoted to testing systems' sensitivity to changes in design parameters. As a rule, high-sensitivity elements are those which should be designed with utmost care. On the other hand, as the mathematical modelling serving for the design process is usually idealized and often inaccurately formulated, some unforeseen alterations may cause the system to behave in a slightly different manner. Sensitivity analysis can help the engineer innovate ways to minimize such system discrepancy, since it starts from the assumption of such a discrepancy between the ideal and the actual system.

Download or read book Characterization of discrete time linear periodically time varying systems written by Kevin W. Baugh and published by . This book was released on 1991 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Analysis and Synthesis of Linear Systems with Time Varying Delay written by John Arthur Kleppe and published by . This book was released on 1970 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: