The Geometry of the Riccati Equation
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES DEPT OF AEROSPACE ENGINEERING
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A study of the matrix Riccati equation is presented without assuming that Q is positive semi-definite. For the autonomous case, a general existence theorem for the equilibrium points of the Riccati equation is proven and their structure is given with respect to the partial ordering induced by the positive semi-definite matrices. Further, a method for finding all equilibria is demonstrated. Necessary and sufficient conditions are given for a global existence of the solution of the Riccati equation, as a function of the initial condition. In the time dependent case, the domain of global existence is shown to contain a certain cone.
- Theoretical Mathematics