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 ε Rⁿ as a state, u ε R^m-control input, ξ ε 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 ^∞∫₀ F(x(t),u(t),ξ(t))dt⩽C(x(0)), ∀T>0 is valid, where F is a given quadratic form Rⁿ×R^m×R^l→R¹ . In particular variants of this inequality lead to the solution of the H^∞-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