The matrix algebraic Lyapunov equation of a forward-pass fixed-interval smoother that uses backward-pass information filter outputs is investigated in continuous-time systems. A necessary and sufficient condition for its solution to yield an asymptotically stable closed-loop system is given. It is then shown that such a condition is more relaxed than that for the backward-pass fixed-interval smoother, which uses forward-pass Kalman filter outputs. Furthermore, some algorithms for solving the algebraic equation are presented using the classical eigenvector approach.
ASJC Scopus subject areas
- Control and Systems Engineering
- Theoretical Computer Science
- Computer Science Applications