A method for determining the optimum linear digital control system with respect to a quadratic performance criterion, when additive disturbances are present, is described. A method of designing multivariable, time varying and/or final value contrrol ystems is presented. This method of design is also advantageous when optimum control must be maintained during the initial start up transient as no assumption concerning steady state was made. The method of estimating the state variables is extended to the case of independent random sampling but the portion concerned with optimum control of a system constrained at the output is only extended to certain special cases. The design method is also extended to adaptive control systems for the case where perfect identification is possible. (Author).

A graduate text providing broad coverage of linear multivariable control systems, including several new results and recent approaches.

This book contains a derivation of the subset of stabilizing controllers for analog and digital linear time-invariant multivariable feedback control systems that insure stable system errors and stable controller outputs for persistent deterministic reference inputs that are trackable and for persistent deterministic disturbance inputs that are rejectable. For this subset of stabilizing controllers, the Wiener-Hopf methodology is then employed to obtain the optimal controller for which a quadratic performance measure is minimized. This is done for the completely general standard configuration and methods that enable the trading off of optimality for an improved stability margin and/or reduced sensitivity to plant model uncertainty are described. New and novel results on the optimal design of decoupled (non-interacting) systems are also presented. The results are applied in two examples: the one- and three-degree-of-freedom configurations. These demonstrate that the standard configuration is one encompassing all possible feedback configurations. Each chapter is completed by a group of worked examples, which reveal additional insights and extensions of the theory presented in the chapter. Three of the examples illustrate the application of the theory to two physical cases: the depth and pitch control of a submarine and the control of a Rosenbrock process. In the latter case, designs with and without decoupling are compared. This book provides researchers and graduate students working in feedback control with a valuable reference for Wiener–Hopf theory of multivariable design. Basic knowledge of linear systems and matrix theory is required.