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

We consider the control of a plant described by a linear system with x /spl epsiv/ R/sup n/ as a state, u /spl epsiv/ R/sup m/-control input, /spl xi/ /spl epsiv/ Rl-unmeasurable input. The considered problem is to give a method of (n-k)-dimensional output controller design so that for the closed-loop system the expression /sup /spl infin///spl int//sub 0/ F(x(t),u(t),/spl xi/(t))dt/spl les/C(x(0)), /spl forall/T>0 is valid, where F is a given quadratic form R/sup n//spl times/R/sup m//spl times/R/sup l//spl rarr/R/sup 1/. In particular variants of this inequality lead to the solution of the H/sup /spl infin//-control problem and the absolute stabilization problem. The solution is based on frequency conditions of n-dimensional robust controllers, due to V. Brusin (1999), and decomposition of the n-dimensional space into a direct sum of subspaces. The application of this method to the spring-connected two-mass system with perturbed stiffness and external disturbances is given.