Variational Analysis, Optimization of Eigenvalues, and Robust Stability

University Of Washington, Seattle WA

Investigators

Abstract

The main focus of the proposed research is the analysis and optimization of various measures of robust stability in linear systems that evolve in time, i.e., linear dynamical systems. Here stability generally refers to the ability of a system to return to steady state after receiving an impulse, e.g., the ability of a structure to stop vibrating after an earthquake. The term "robust stability" refers to notions of stability that attempt to balance the transient stability of a system with its asymptotic stability. The asymptotic stability of a linear system has a well-established relationship to the eigenvalues of the underlying system. However, it has long been recognized in linear dynamics that when the associated linear transformation is highly non-normal the eigenvalues give little or no information about the transient behavior of the system. This transient behavior can be quite unacceptable from the perspective of engineering design and control. This has given rise to the modern focus on transient stability, which generally refers to such properties as bounded transient peaks and/or bounded transient growth/decay rates. The PI and his collaborators have already established a rich foundation of techniques, results, and numerical tools for further progress in this research. They propose to continue this work and to provide efficient numerical tools for engineering design and control practitioners.