We review the popular Linear Gaussian Quadratic (LQG) controller design for DPS and its shortcomings. In particular, its applicability is essentially restricted to exponentially stabilizable and detectable DPS with finite-rank bounded input and output operators. As an alternative, we propose a new practical control design that is applicable to DPS with unbounded, finite-rank input and output operators, provided that the generator has finitely many unstable eigenvalues and satisfies the spectrum determined growth assumption.
- INFINITE-DIMENSIONAL SYSTEMS
- RICCATI EQUATION