Studies On The Stability Of Time Varying Systems
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| Author | : Peter Dorato |
| Publisher | : |
| Total Pages | : 156 |
| Release | : 1961 |
| Genre | : Stability |
| ISBN | : |
The concept of short-time stability finds application in missile and satellite systems where operating times are often of finite duration. Short-time stability assures, in a finite time interval, that all inputs bounded by a prescribed constant Greek epsilon result in outputs bounded by a second prescribed constant. The study of short-time stability is divided into two categories: undriven systems and driven systems. Undriven systems are represented by a set of differential equations. Sufficient conditions for short-time stability are given in terms of the coefficients. Driven systems are represented by their impulse response. A necessary and sufficient condition for short-time stability in driven systems is given directly in terms of impulse response. Sufficient conditions for short-time stability in feedback systems, in terms of the open loop impulse response are also included. In addition the concept of shorttime C-equivalence, essentially a structural stability concept, is introduced. Necessary and sufficient conditions for two systems to be short-time C-equivalent are presented. (Author).
| Author | : Bernhard Bussmann |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 1971 |
| Genre | : Linear systems |
| ISBN | : |
The stability of systems is investigated which can be described by differential equations consisting of a linear time- varying part and one nonlinear term. First, only the linear part is considered. Definition and properties of the impulse response are discussed in detail. Closed form solutions are evaluated for some special systems. For the general case, approximations are determined by comparing two integral equations. Then, utilizing the results of the linear part, an integral equation is set up for the complete system, including the nonlinear term. Sufficient stability conditions are derived. It is shown that the appropriate Volterra series is convergent unde relatively weak restrictions.
| Author | : John A. Richards |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 186 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3642818730 |
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.
| Author | : Kostas S. Tsakalis |
| Publisher | : |
| Total Pages | : 302 |
| Release | : 1993 |
| Genre | : Science |
| ISBN | : |
| Author | : Yuriy Shmaliy |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 649 |
| Release | : 2007-09-23 |
| Genre | : Technology & Engineering |
| ISBN | : 1402062729 |
This work offers students at all levels a description of linear, nonlinear, time-invariant, and time-varying electronic continuous-time systems. As an assemblage of physical or mathematical components organized and interacting to convert an input signal to an output signal, an electronic system can be described using different methods offered by the modern systems theory. To make possible for readers to understand systems, the book systematically covers the major foundations of the systems theory.
| Author | : Henri Bourlès |
| Publisher | : Springer |
| Total Pages | : 653 |
| Release | : 2011-04-21 |
| Genre | : Technology & Engineering |
| ISBN | : 3642197272 |
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.
| Author | : Maria Tomas-Rodriguez |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 303 |
| Release | : 2010-02-04 |
| Genre | : Mathematics |
| ISBN | : 184996100X |
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.
| Author | : Keqin Gu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 367 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 1461200393 |
This book is a self-contained presentation of the background and progress of the study of time-delay systems, a subject with broad applications to a number of areas.
| Author | : Francesco Amato |
| Publisher | : John Wiley & Sons |
| Total Pages | : 184 |
| Release | : 2018-10-08 |
| Genre | : Technology & Engineering |
| ISBN | : 1119140528 |
Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.
| Author | : Belghasem Abdulgalil Dawaghi |
| Publisher | : |
| Total Pages | : 188 |
| Release | : 1974 |
| Genre | : |
| ISBN | : |
