Progress in polynomial optimisation

The polynomial equation approach to the design of optimal multivariable control systems was pioneered during the 1970´s by Kucera. This approach provides a distinctive alternative to the state-space and Wiener-Hopf optimisation procedures. The contribution of this paper is twofold: the author reviews and summarises the major advances made in the polynomial equation approach H₂ optimisation during the 1980´s for multivariable systems; and presents new results concerned with the solution of the H₂-optimal control problem for the `standard´ control structure