Optimal low-order feedback controllers for discrete-time linear systems with inaccessible state

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This paper considers the problem of designing optimal low-order dynamical feedback controllers for a class of discrete-time linear time-invariant systems with inaccessible state. The performance index is taken to be the expectation, with respect to the initial state, of the standard quadratic one for the discrete-time regulator. Necessary conditions for optimality are derived and an optimal solution is shown to exist. In order to implement the optimal controller it is required to solve two non-linear matrix algebraic equations. The design is illustrated by a simple numerical example.