On Determining the Robust Pole Locations of Uncertain Systems: An LMI Approach

摘要

This paper addresses the problem of determining the robust pole locations of systems with structured uncertainties. Different from the researches using methods based on the LMI-region, the bound of the pole cluster around each nominal system pole is studied, which can provide more clear dynamic information of uncertain systems. Utilizing the matrix spectral radius property and the linear matrix inequality (LMI) method, the problem of determining the discs of equal radius which contain the pole clusters of the uncertain system is formulated as an LMI generalized eigenvalue problem (GEVP). An improved method is then proposed for obtaining a more accurate estimate of the individual discs containing each pole cluster using an LMI eigenvalue optimization approach. Finally, the problem of determining the perturbation bounds which ensure that the robust pole clusters remain within certain pre-specified discs is formulated as another LMI GEVP. The validity of the proposed approach is demonstrated by way of a numerical example.