Numerical algorithms for generalized eigenvalue problems of even structure with application in robust control of descriptor systems

The aim of the project is the development of efficient structure-preserving numerical methods for the solution of generalized eigenvalue problems of even structure, as well as their use in the construction of efficient numerical procedures for the robust control of continuous-time and discrete-time general descriptor systems (under inclusion of time retardations).

The first main point of the project is the investigation of the theoretical basis of the H_∞-theory for singular continuous-time and discrete-time descriptor systems under inclusion of retarded arguments. Especially it has been shown that the solution of this task can be reached by the calculation of generalized Lagrange-subspaces for matrix pencils of even structure. The second main point is the development, investigation and implementation of numerical algorithms for generalized eigenvalue problems of even structure and their error analysis. Especially the existence, uniqueness and stability of generalized Lagrange-subspaces for matrix pencils of even structure, as well as the accompanying perturbation theory and error analysis, will be examined.

Together both project parts give the base of design procedures for optimal H_∞-controllers, both for general linear continuous-time and for discrete-time (retarded) descriptor systems.