The subject of this volume is the design of optimal and robust control systems using system models which are represented by polynomial matrices, the polynomial approach being close to the frequency domain design method that engineers use in practice. The subject matter ranges from fundamental systems theory to application problems. The text introduces the polynomial systems approach to solving both control and filtering problems. The benefits of frequency domain analysis and design procedures are demonstrated and the power of polynomial modelling procedures in applications is revealed. Both H2 and H (infinity) design methods are considered, involving both scalar and multivariable problem solutions.