The transfer function approach is widely used in classical control theory for its easy handling and physical meaning. Although the use of transfer functions is well-established for linear time-invariant systems, it is not suitable for non-stationary systems among which are sampled-data systems and processes with periodically varying coefficients. Computer-controlled continuous-time processes are a very important subset of periodic sampled-data systems which are not treatable using ordinary transfer functions.

Having established the ability of the parametric transfer function to solve this problem for single-input, single-output systems in previous work, the authors extend these methods, which incorporate time-dependence, to the idea of the parametric transfer matrix in a complete exposition of analysis and design methods for multiple-input, multiple-output (MIMO) sampled-data systems.

Multivariable Computer-controlled Systems is divided into three parts:

• Preliminary algebraic material describing the established fundamentals of polynomial and rational matrices necessary for the understanding of later chapters.
• Control problems, important in their own right but which also have a substantial bearing on what follows (eigenvalue assignment and the use of z- and zeta-transforms in discrete systems).
• Frequency methods for the investigation of MIMO sampled-data systems (parametric discrete-time models; stability; stochastic methods; H2 optimization and L2 design).

Appendices covering basic mathematical formulae and the description of two MATLABA(R) toolboxes round out this self-contained guide to multivariable control systems.

Of specialinterest to researchers in automatic control and to development engineers working with advanced control technology, Multivariable Computer-controlled Systems will also interest mathematical control theorists and graduate students studying advanced methods of computer-based control.

This book is devoted to the problem of sampled-data control of finite-dimensional linear continuous periodic (FDLCP) objects. It fills a deficit in coverage of this important subject. The methods presented here are based on the parametric transfer matrix, which has proven successful in the study of sampled-data systems with linear time-invariant objects. The book shows that this concept can be successfully transferred to sampled-data systems with FDLCP objects. It is set out in five parts: * * an introduction to the frequency approach for the mathematical description of FDLCP objects including the determination of their structure and their representation as a serial connection of periodic modulators and a linear time-invariant object; * construction of parametric transfer matrix for different types of open and closed sampled-data systems with FDLCP objects; * the solution of problems of causal modal control of FDLCP objects based on the mathematical apparatus of determinant polynomial equations; * consideration of the problem of constructing a quadratic quality functional for the H2-optimization problem of a single-loop synchronous sampled-data system with control delay; * description of the general H2-optimization procedure. Necessary mathematical reference material is included at relevant points in the book. Sampled-Data Control for Periodic Objects is of use to: scientists and engineers involved in research and design of systems of systems with FDLCP objects; graduate students wishing to broaden their scope of competence; their instructors; and mathematicians working in the field of control theory.

This book introduces the reader to a novel method of mathematical description, analysis and design of digital control systems, which makes it possible to take into account, in the most complete form, specific features of interaction between continuous-time and discrete time processes.

Computer-Controlled Systems with Delay is a systematic study of the problems of analysis and synthesis for multidimensional sampled-data (SD) systems with delay. It is based on the frequency polynomial method, in which the concept of a parametric transfer matrix (PTM) plays a key role. Until now, no alternative general methods have been available to solve the above problems. The text is divided into three parts: background information from the theory of polynomial and rational matrices, helps the reader to acquire the basic understanding necessary to use the main content of the book without addressing additional sources; methods for the mathematical description of multidimensional SD systems with delay, based on the concept of the PTM; and optimization methods for multidimensional SD systems with delay, including H2 and L2 optimization as well as H2 optimization for colored input signals. The monograph is completed by three appendices. An algorithm for constructing the set of pathological sampling periods for a continuous SISO object with delay is provided first. MATLAB (R)-toolbox algorithms representing methods described in the book and application examples for selected optimization problems are given in the second. A solution to the problem of guaranteeing the required performance in a class of stochastic disturbances for SD systems with delay is considered in the third. Computer-Controlled Systems with Delay is intended for engineers, scientists and teachers working in modern control theory. It will also benefit post-graduate students taking courses in related disciplines. The book continues the description of the authors' research results on developing methods for SD systems theory which are based on the PTM concept and published in the monographs Computer Controlled Systems and Multivariable Computer-controlled Systems.