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\({\mathcal H}_ 2\) control for discrete-time systems optimality and robustness. (English) Zbl 0782.49022

Summary: This paper proposes a new approach to determine \({\mathcal H}_ 2\) optimal control for discrete-time linear systems, based on convex programming. It is shown that all stabilizing state feedback control gains belong to a certain convex set, well-defined in a special parameter space. The linear quadratic problem can be then formulated as the minimization of a linear objective over a convex set. The optimal solution of this convex problem furnishes, under certain conditions, the same feedback control gain which is obtained from the classical discrete-time Riccati equation solution. Furthermore, the method proposed can also handle additional constraints, for instance, the ones needed to assure asymptotical stability of discrete-time systems under actuators failure. Some examples illustrate the theory.

MSC:

49N10 Linear-quadratic optimal control problems
93C55 Discrete-time control/observation systems
93B35 Sensitivity (robustness)
90C25 Convex programming
93C05 Linear systems in control theory
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References:

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