A method of reduced order robust controller design, based on frequency conditions

It's considered controlled plant described by a linear system with x is an element of R-n as state, u is an element of R-m - control input, xi is an element of R-l - unmeasurable input. The considered problem is to give a method of (n - k)-dimensional output controllers design so that for the closed-loop system it is valid (0)integral (infinity) F(x(t),u(t),xi (t))dt less than or equal to C(x(0)), For AllT > 0, where F is given quadratic form R-n x R-m x R-l --> R-1. In particular variants this inequality leads to solution H-infinity-control problem and the absolute stabilization problem. The solution is based on frequency conditions of n-dimensional robust controllers existence, early received V. Brusin, and decomposition n-dimensional space into a direct sum of subspaces. The appication of this method to spring-connected two-mass system with perturbed stiffness and external disturbances is given.