Simplified Lyapunov matrix equation with applications to the control of distributed-parameter systems

The Lyapunov matrix equation is shown to be of importance in generating the optimal gains for distributed-parameter feedback control systems with controllers based on the values of the state variables at discrete points. It is shown that the Lyapunov matrix equation can be considerably reduced for such systems. In a typical example, the number of unknowns is reduced from 1225 to 49.