Optimal distributed control systems design

A systematic technique is proposed for designing optimal control systems for the class of linear distributed parameter systems (DPS), such as vibrations, and shock waves. The dynamics of the system is expressed by a set of interrelated difference equations in the form of a discrete state space model which is ideal for designing control systems. The control strategy and the degree of controllability of the system are set forth by a set of performance criteria for the system. The control law is derived and it is optimally distributed in space. Requirements for selecting an appropriate set of weighting factors for the performance criterion are provided. Conditions for the system stability are established.