Designing Stabilizing Controllers for Uncertain Systems using the Riccati Equation Approach

A useful technique for determining a linear feedback control law which stabilizes an uncertain system is the Riccati equation approach of Petersen and Hollot [1,2]. They consider systems with time-varying uncertainty in the system matrix and obtain the constant feedback gains for the linear stabilizing controller in terms of the solution of a Riccati equation. Here we extend this technique to include problems with time-varying uncertainty in the input connection matrix. Several examples are included to demonstrate the efficacy of this result.