# Linear Discrete-Time Systems - \(H_\infty \) Dynamic Output-Feedback Control with Preview

## Abstract

The theory of preview tracking control is applied for the solution of the dynamic output-feedback control problem of linear discrete-time systems for both: finite-horizon and stationary cases. Based of the solution of the state-feedback control problem and a specially devised version of the bounded real lemma for systems with tracking signals, three preview patterns are explored. The latter include the simplest case where the tracking signal is measured on line and two additional cases where the tracking signal is either previewed in a fixed interval ahead or it is perfectly known in advance along the finite horizon interval given in the system. The principle method of solution for all the latter three preview patterns is that the controller plays against nature which chooses the initial condition and the energy-bounded disturbances.

## Keywords

\(H_\infty \) control Discrete-time systems Tracking preview## References

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