This paper considers the robustness of a feedback connection of a known linear parameter varying system and a perturbation. A sufficient condition is derived to bound the worst-case gain and ensure robust asymptotic stability. The input/output behavior of the perturbation is described by multiple integral quadratic constraints (IQCs). The analysis condition is formulated as a dissipation inequality. The standard approach requires a non-negative definite storage function and the use of ‘hard’ IQCs. The term ‘hard’ means that the IQCs can be specified as time-domain integral constraints that hold over all finite horizons. The main result demonstrates that the dissipation inequality condition can be formulated requiring neither a non-negative storage function nor hard IQCs. A key insight used to prove this result is that the multiple IQCs, when combined, contain hidden stored energy. This result can lead to less conservative robustness bounds. Two simple examples are presented to demonstrate this fact.
|Original language||English (US)|
|Number of pages||15|
|Journal||International Journal of Robust and Nonlinear Control|
|State||Published - Nov 10 2016|
Bibliographical noteFunding Information:
This work was partially supported by the AFOSR under the grant entitled A Merged IQC/SOS Theory for Analysis of Nonlinear Control Systems, Dr. Fahroo technical monitor. This work was also partially supported by the National Science Foundationunder Grant No. NSF-CMMI-1254129 entitled CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms.
- linear parameter varying systems
- robust control
- uncertain systems