Dominant and recessive solutions of symmetric three term recurrences. (English) Zbl 0797.93022

Summary: Dominant and recessive solutions are defined for matrix three term recurrences \[ - K_ n X_{n+1}+ B_ n X_ n- K^ T_{n-1} X_{n- 1}= 0. \] Eventual disconjugacy is shown to imply existence of a recessive solution at \(\infty\) and, furthermore, that an associated Riccati equation \[ W_{n+1}= A_ n+ E^{-1}_ n W_ n(W_ n+ C_{n- 1})^{-1} C_{n-1}(E^ T_ n)^{-1} \] has an eventually minimal solution \(W^ -_ n\). Riccati equations of this form with \(A_ n\) and \(C_ n\) positive definite arise in the discrete regulator problem.


93C15 Control/observation systems governed by ordinary differential equations
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