Brief Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems
Automatica (Journal of IFAC)
Brief Constrained quadratic state feedback control of discrete-time Markovian jump linear systems
Automatica (Journal of IFAC)
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This paper considers ${\cal H}_{2}/{\cal H}_\infty$ control problems involving discrete-time uncertain linear systems. The uncertain domain is supposed to be convex bounded, which naturally covers, as a particular case, the important class of interval matrices. The ${\cal H}_\infty$ guaranteed-cost control problem, solved for this class of uncertain systems, under no matching conditions, can be stated as follows: determine a state feedback gain (if one exists) such that the $\Hi$ norm of a given transfer function remains bounded by a prespecified level for all possible models. In the same context, problems on the determination of the smallest ${\cal H}_\infty$ upper bound and the minimization of an ${\cal H}_2$ cost upper bound subject to ${\cal H}_\infty$ constraints are also addressed. The results follow from the fact that those problems are convex in the particular parametric space under consideration. Some examples illustrate the theory.