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The discrete-time linear control systems have been applied in the wide area of applications such as engineering, economics, biology. Such type systems have been intensively considered in the control literature in both the deterministic and the stochastic framework. The stability and optimal control of stochastic differential equations withMarkovian switching has recently received a lot of attention, see Freiling and Hochhaus [8], Costa, Fragoso, and Marques [2], Dragan and Morozan [4, 5]. The equilibrium in these discrete-time stochastic systems can be found via the maximal solution of the corresponding set of discrete-time Riccati equations.

Iterations for a General Class of Discrete-Time Riccati-Type Equations: A Survey and Comparison