Simultaneous stabilization is an important problem in the design of robust controllers. It is the problem of designing a single feedback controller which will simultaneously stabilize every member of a finite collection of liner time-invariant systems. This provides simplicity and reliability which is desirable in aerospace applications. It can be used as a back-up control system in sophisticated airplanes, or an inexpensive primary one for small aircraft. In this work the robustness of the simultaneous stabilization problem, known as the Robust Simultaneous Stabilization (RSS) problem, is addressed. First, an optimization methodology for finding a solution to the Simultaneous Stabilization (SS) problem is proposed. Next, in order to provide simultaneous stability while maximizing the stability robustness bounds, a multiple-robustness optimization design methodology for the RSS problem is presented. The two proposed design methodologies are then compared in terms of robustness of the designed controller.

Simultaneous stabilization is an important problem in the design of robust controllers. It is the problem of designing a single feedback controller which will simultaneously stabilize every member of a finite collection of liner time-invariant systems. This provides simplicity and reliability which is desirable in aerospace applications. It can be used as a back-up control system in sophisticated airplanes, or an inexpensive primary one for small aircraft. In this work the robustness of the simultaneous stabilization problem, known as the Robust Simultaneous Stabilization (RSS) problem, is addressed. First, an optimization methodology for finding a solution to the Simultaneous Stabilization (SS) problem is proposed. Next, in order to provide simultaneous stability while maximizing the stability robustness bounds, a multiple-robustness optimization design methodology for the RSS problem is presented. The two proposed design methodologies are then compared in terms of robustness of the designed controller.