Exact observability/exact detectability and spectrum assignment of stochastic systems
In the present paper, we study the exact observability and exact detectability for stochastic Itô systems, which have state-dependent noises in both state equation and measurement equation. Some results for the exact observability and exact detectability are obtained, respectively. We also consider the problem of spectrum assignment and give a necessary and sufficient condition on ensuring all the spectra in a specified disk. Finally, the relationship between the solutions of generalized Lyapunov equation (GLE) and generalized algebraic Riccati equation (GARE) is considered.