In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown that in general the set of solutions that solve the problem constitutes a manifold. This feedback formulation of the optimization problem is natural in the context of differential games and we provide a characterization of feedback Nash equilibria in a deterministic context.
|Place of Publication||Tilburg|
|Number of pages||20|
|Publication status||Published - 2008|
|Name||CentER Discussion Paper|
- linear quadratic optimal control
- descriptor systems
- static stabilizing state feedback control
Engwerda, J. C., Salmah, Y., & Wijayanti, I. E. (2008). The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems. (CentER Discussion Paper; Vol. 2008-90). Operations research.