  The concept of turnpike connects the solution of long but finite time horizon
optimal control problems with steady state optimal controls. A key ingredient
of the analysis of the turnpike is the linear quadratic regulator problem and
the convergence of the solution of the associated differential Riccati equation
as the terminal time approaches infinity. This convergence has been
investigated in linear systems theory in the 1980s. We extend classical system
theoretic results for the investigation of turnpike properties of standard
state space systems and descriptor systems. We present conditions for turnpike
in the nondetectable case and for impulse controllable descriptor systems. For
the latter, in line with the theory for standard linear systems, we establish
existence and convergence of solutions to a generalized differential Riccati
equation.
