Nonnegative-Definite Steady-State Solutions of Singular Matrix Riccati Equations in Discrete Time-Invariant Systems

Abstract

Matrix Riccati equations arising in optimal filtering and control problems of discrete time-invariant systems with possibly singular state transition matrices are considered in this paper.
An algebraic approach based on a formulation as a generalized rather than an ordinary eigenvalue problem is employed.
Existence conditions are derived of nonnegative definite steady-state solutions together with relevant properies to the generalized eigenvalue problem. Also, a construction method of all such solutions is given. It is seen that the results associated with nonsingular state transition matrices are generalized in a natural fashion.