Left invertibility and invertible solutions of the Lyapunov equation
نویسنده
چکیده
If the solution of a Lyapunov or Riccati equation corresponding to a finite-dimensional system is invertible, then this leads to additional properties of this system. For infinite-dimensional systems these results do not need to hold. We show that it is necessary to put some additional conditions on the spectrum of the system operator A. For instance, if this operator has compact resolvent, then the results known for finite-dimensional systems extend to infinite-dimensional ones. Using this result, we obtain more insight in Lyapunov and Riccati equations for well-posed linear systems.
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تاریخ انتشار 2011