27th Conference of the International Linear Algebra Society (ILAS 2026)

Riccati Differential Equations, State Transition Matrices, and State Covariance Matrices

May 19, 2026, 4:35 PM

25m

Goodwin Hall 145 (Virginia Tech)

Minisymposium Talk Matrix Inequalities, Matrix Equations, and Their Applications Matrix Inequalities, Matrix Equations, and Their Applications

Speaker

Fengjiao Liu (FAMU-FSU College of Engineering)

Description

In this talk, we first investigate the maximal interval of existence for the solution of a symmetric matrix Riccati differential equation. Then, we apply this result to study the reachability of the closed-loop state transition matrix for a linear time-varying system over a finite time interval. Under a mild assumption, we characterize the set of closed-loop terminal state transition matrices reachable from the identity matrix using controls of the state feedback form. Lastly, we provide the set of terminal state covariance matrices reachable from a given positive definite initial state covariance matrix when the linear system is not necessarily controllable.