## 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.

### MSC:

 93C15 Control/observation systems governed by ordinary differential equations

### Keywords:

Riccati equation; discrete regulator problem
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