Stability radius optimization and loop transfer recovery for uncertain dynamic systems

The difficult problem of robust stabilization and performance of dynamic systems under structured uncertainty motivates one to look into alternative solutions. Due to the conservatism and limitation associated with two lines of research; namely, robust recovery of LQR in LQG design and quadratic stabilization, we introduce a new feasible solution to this problem. The main idea is to design controllers for robust stabilization of uncertain systems such that the resulting closed-loop systems are structurally constraint to certain classes of systems with desirable properties. The special classes of systems considered in this paper are nonnegative and Metzlerian. We make use of previously reported results for these classes of systems and introduce a new design approach called stability radius optimization loop transfer recovery, SRO/LTR, which can be regarded as a two step procedure similar to the LQG/LTR method. However, the flexibility offered by the SRO allows constraints to be imposed on the structure of the resulting closed-loop target feedback loop.