Sampled-Data Control for Periodic Objects (2022)

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 thefield of control theory.