This book showcases the versatility and effectiveness of polynomial methods in control and filtering, an area that has received less attention compared to the Wiener-Hopf transfer-function and state-space approaches based on Riccati equations.
It offers comprehensive coverage of the polynomial equation approach for various linear control and filtering problems. The key feature of this method is representing systems in fractional form using transfer functions, which naturally leads to parameterizing all suitable feedback controllers for a given problem as a Diophantine equation over polynomials. This direct parameterization is carried through to the synthesis of controllers and filters, as well as to the computer implementation of numerical algorithms.
The book is intended for students, researchers, and engineers with a background in control, systems theory, or signal processing, and could serve as the foundation for a graduate-level course in optimal control and filtering. It starts with tutorial-level background material and progresses through recent theoretical and practical advances to detailed numerical algorithms.
