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A Discrete-Time Approach for System Analysis is a five-chapter text that considers the underlying principles and application of a discrete-time approach to system analysis. Chapter 1 presents several different unit functions that are used in practice and describes how to obtain a closed form for the sequence of unit functions by using the E- and the z-transforms. This chapter also compares some aspects of spectral analysis and impulse analysis, and finally, discusses some aspects of interpolation between sampled data of the functions by impulse analysis techniques. Chapter 2 provides the functional operations using the sequences of unit functions, namely, addition, subtraction, multiplication, convolution, deconvolution, integration, and differentiation. Chapter 3 examines linear, time-varying, nonlinear and partial differential equations, and the use of the discrete time approach to solve these equations. Chapters 4 and 5 discuss several applications of impulse analysis to control problems, basically, system analysis and identification. This book is particularly useful to engineers with an introduction to some techniques for finding solutions of certain time-invariant, time-varying, and nonlinear differential equations arising in physical systems.
This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
Most queuing analyses performed in the literature are based on characterization of queueing phenomena in continuous-time items. Recently in the telecommunication industries, BISDN (broadband integrated services digital network) has received considerable attention since it can provide a common interface for future communication needs including video, data, and speech. Since information in BISDN is transported by means of dicsrete units of 53-octet ATM (asynchronous transfer mode) cells, interests in discrete-time systems have increased. Discrete-Time Models for Communication Systems Including ATM provides a general framework for queueing analyses of dicrete-time systems. After a brief look at past studies of discrete-time systems, a detailed description and analysis are presented for a generic discrete-time model with a single server, arbitrary service times and independent arrivals. The book then follows a less stringent approach and focuses more on the average statistics and on different queueing disciplines. Conventional first-in-out and last-in-first-out disciplines are discussed in terms of the average statistics. Systems with multiple classes of messages without class-dependent priorities are considered to establish a discrete-time conservation law. Multiple classes with priorities are also considered to derive performance measures of priority scheduling disciplines. Finally, a multi-queue system with cyclic service is analyzed in the context of round-robin service ordering. This is followed by analyses of discrete-time queueing systems with `more complicate' input and output processes. Specifically, single-server systems are investigated whereby either the arrivals or the server is subject to random interruptions. Results are mainly obtained in terms of generating functions and mean values of the principal performance measures. The influence of the nature of the arrival correlation and the server interruptions on the queueing behavior is discussed. Finally, the book explores queueing models directly associated with ATM switches and multiplexers. This book is a valuable reference and may be used as a text for and advanced course on the subject.
More and more digital devices are being used for informa tion processing and control purposes in a variety of systems applications, including industrial processes, power networks, biological systems and communication networks. This trend has been helped by the advent of microprocessors and the consequent availability of cheap distributed computing power. For those applications, where digital devices are used, it is reasonable to model the system in discrete-time. In addition there are other application areas, e.g. econometric systems, business systems, certain command and control systems, environmental systems, where the underlying models are in discrete-time and here discrete-time approaches to analysis and control are the most appropriate. In order to deal with these two situations, there has been a lot of interest in developing techLiques which allow us to do analysis, design and control of discrete-time systems. This book provides a comprehensive treatment of discrete time dynamical systems. It covers the topics of modelling, optimization techniques and control design. The book is designed to serve as a text for teaching at the first year graduate level. The material included is organized into eight chapters.
Analysis and Synthesis of Polynomial Discrete-time Systems: An SOS Approach addresses the analysis and design of polynomial discrete-time control systems. The book deals with the application of Sum of Squares techniques in solving specific control and filtering problems that can be useful to solve advanced control problems, both on the theoretical side and on the practical side. Two types of controllers, state feedback controller and output feedback controller, along with topics surrounding the nonlinear filter and the H-infinity performance criteria are explored. The book also proposes a solution to global stabilization of discrete-time systems. - Presents recent developments of the Sum of Squares approach in control of Polynomial Discrete-time Systems - Includes numerical and practical examples to illustrate how design methodologies can be applied - Provides a methodology for robust output controller design with an H-infinity performance index for polynomial discrete-time systems - Offers tools for the analysis and design of control processes where the process can be represented in polynomial form - Uses the Sum of Squares method for solving controller and filter design problems - Provides MATLAB® code and simulation files of all illustrated example
This book presents recent theoretical advances in the analysis and synthesis of discrete-time switched systems under the time-dependent switching scheme, including stability and disturbance attenuation performance analysis, control and filtering, asynchronous switching, finite-time analysis and synthesis, and reachable set estimation. It discusses time-scheduled technology, which can achieve a better performance and reduce conservatism compared with the traditional time-independent approach. Serving as a reference resource for researchers and engineers in the system and control community, it is also useful for graduate and undergraduate students interested in switched systems and their applications.
Reliability Modelling and Analysis in Discrete Time provides an overview of the probabilistic and statistical aspects connected with discrete reliability systems. This engaging book discusses their distributional properties and dependence structures before exploring various orderings associated between different reliability structures. Though clear explanations, multiple examples, and exhaustive coverage of the basic and advanced topics of research in this area, the work gives the reader a thorough understanding of the theory and concepts associated with discrete models and reliability structures. A comprehensive bibliography assists readers who are interested in further research and understanding. Requiring only an introductory understanding of statistics, this book offers valuable insight and coverage for students and researchers in Probability and Statistics, Electrical Engineering, and Reliability/Quality Engineering. The book also includes a comprehensive bibliography to assist readers seeking to delve deeper. - Includes a valuable introduction to Reliability Theory before covering advanced topics of research and real world applications - Features an emphasis on the mathematical theory of reliability modeling - Provides many illustrative examples to foster reader understanding