How to Decompose Semi-definite Discrete-Time Algebraic Riccati Equations

摘要

The ill-posedness of the semi-definite discrete-time algebraic Riccati equation can be related to the zeros of an associated linear time-invariant system. When there are arbitrary zeros the solution is often discontinuous, and when there are zeros on the unit circle the soluiion is often not differentiable with respect to the parameters of the equation. In this paper it is discussed how to decompose a potentially illposed equation into a trivial part and a reduced- order wellposed equation. The reduction algorithm also provides a novel constructive proof of the existence of a solution to the discrete-time algebraic Riccati equation. The reduction scheme has been implemented in Matlab and evaluated on some examples. It is seen that it pedorms well.