An LQR approach to robust control of linear systems with uncertain parameters

Robust state feedback controllers for linear time-invariant systems with uncertain parameters are considered. Both matched and unmatched uncertainty structures are studied. A basic tool of analysis is a special auxiliary LQR problem without uncertainties. The solution to this problem guarantees unconditionally robust stabilization in the matched case. In the unmatched case, if some testable sufficient conditions are satisfied, the solution of the LQR problem is robustly stabilizing as well. Moreover, robust pole placement into an arbitrary left halfplane is constructively proved to be achievable in the matched case. In the unmatched case, our sufficient conditions for robust stabilization can be modified for the robust pole placement problem but they become void if the required set, into which the eigenvalues ought to be placed, is too far away from the imaginary axis