Computational methods for the H∞ control of distributed systems

Some explicit design examples using a frequency-domain (skew Toeplitz) approach in the H^∞ optimization of distributed systems are discussed. The emphasis is on the computational aspects of this methodology, which allows one to reduce infinite-dimensional design problems to finite-dimensional matrix and polynomial operations. A very general outline of what is involved in skew Toeplitz theory is given. It is shown how the solution of the H ^∞ optimization problem for distributed plants can be derived from a finite system of linear equations called the singular system. This theory is applied to a weighted two-block design for unstable plant models with delay. A mixed sensitivity design for a flexible beam modeled by the Euler-Bernoulli equation with Kelvin-Voigt damping is discussed. A delay is included in the model