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On computing the stabilizing solution of a class of discrete-time periodic Riccati equations. (English) Zbl 1312.93068
Summary: This paper addresses the problem of solving a class of periodic discrete-time Riccati equation with an indefinite sign of its quadratic term. Such an equation is closely related to the so-called full-information $$H_\infty$$ control of discrete-time periodic systems. A globally convergent iterative algorithm with a local quadratic convergence rate is proposed for this purpose. An application to the problem of $$H_\infty$$ filtering of discrete-time periodic systems is also developed and illustrated via a numerical example.

##### MSC:
 93C55 Discrete-time control/observation systems 93B40 Computational methods in systems theory (MSC2010) 39A23 Periodic solutions of difference equations
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