Stabilization of Linear Systems with Structured Perturbations
CALIFORNIA INST OF TECH PASADENA CONTROL AND DYNAMICAL SYSTEMS
Pagination or Media Count:
The problem of stabilization of linear systems with bounded structured uncertainties are considered in this paper. Two notions of stability, denoted quadratic stability Q-stability and stability, are considered, and corresponding notions of stabilizability and detectability are defined. In both cases, the output feedback stabilization problem is reduced via a separation argument to two simpler problems full information I and full control FC. The set of all stabilizing controllers can be parametrized as a linear fractional transformation LFT on a free stable parameter. For Q-stability, stabilizability and detectability can in turn be characterized by Linear Matrix Inequalities LMIs, and the FI and FC Q-stabilization problems can be solved using the corresponding LMIs. In the standard one-dimensional case the results in this paper reduce to well-known results on controller parametrization using state-space methods, although the development here relies more heavily on elegant LFT machinery and avoids the need for coprime factorizations.
- Numerical Mathematics