Nonlocal stability analysis problems in the presence of multiple isolated equilibria or in the presence of nontrivial dynamic or geometric constraints appear in a wide variety of applications ranging from electrical circuits to biological systems. Establishing nonlocal convergence and stability results in such situations is a difficult task.
In this talk we discuss a recent result which can handle such intrinsically nonlinear situations. The result has turned out to be especially useful in stability analysis problems involving a two-step design procedure, where typically, the first step involves designing (shaping) a desired nontrivial steady-state behavior in a certain region in the state space and the second step renders this region attractive. Applications which fall into this category are the design of synchronization laws, nonlinear output regulators, or the design of optimization algorithms. In this talk, we discuss the basic idea behind the result and we show how it applies to the applications mentioned above.
Christian Ebenbauer received his MS (Dipl.-Ing.) in Telematics (Electrical Engineering and Computer Science) from Graz University of Technology, Austria, in 2000 and his PhD (Dr.-Ing.) in Mechanical Engineering from the University of Stuttgart, Germany, in 2005. After having completed his PhD, he was a Postdoctoral Associate and an Erwin Schrodinger Fellow at the Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, USA. Since 2009, he is a professor at the Institute for Systems Theory and Automatic Control, University of Stuttgart, Germany. His research interests lie in the areas of dynamical systems, control theory, optimization and computation.