Synthesis of robust linear-quadratic Gaussian controllers (Q1883922)

A problem is considered for the synthesis of robust linear-quadratic Gaussian controllers optimizing a quadratic quality criterion and ensuring an \(H_\infty\)-norm of the transfer function of a closed-loop system that does not exceeds a preassigned value. The known synthesis methods rely on the solution of the Riccati \(H_\infty\)-equation. The monotonicity of the dependence of the stabilizing solution of the Riccati \(H_\infty\)-equation on weighting matrices and multipliers of the quality criterion is shown. An iterative algorithm is put forward for the synthesis of robust linear-quadratic Gaussian controllers. The algorithm relies on the solution of the linear-quadratic Gaussian-Riccati equation only.