The normal matrix approach to the design of multivariable robust control systems

It has been proved that the normality of the open-loop transfer function matrix is at least a sufficient condition for best robustness of a control system in the H/sub /spl infin// index sense. On the above basis this paper presents a new approach to the design of multivariable control system-the "optimization of parametrized normal matrix (OPNORM)" design method. The open-loop transfer function matrix of a system consists of two parts: a set of eigenfunctions and an eigenvector matrix. Each of them plays its specific role in the behaviour of the system. The unitarity of the eigenvector matrix guarantees the normality of the transfer function matrix, and hence guarantees the system robustness, while the eigenfunctions determine the system stability and dynamic performance. By systematically searching among unitary matrices and among stable eigenfunctions, a controller can be found which not only guarantees system stability and satisfactory dynamic performance, but also gives best system robustness in the sense of minimum H/sub /spl infin// norm index. The controller thus obtained is usually very much simpler than that designed by the H/sub /spl infin// approach. An example is given to illustrate the new design method.<>