\(\ell ^1\)-optimal control for multirate systems under full state feedback. (English) Zbl 1274.93098

Summary: This paper considers the minimization of the \(\ell ^{\infty }\)-induced norm of the closed loop in linear multirate systems when full state information is available for feedback. A state-space approach is taken and concepts of viability theory and controlled invariance are utilized. The essential idea is to construct a set such that the state may be confined to that set and that such a confinement guarantees that the output satisfies the desired output norm conditions. Once such a set is computed, it is shown that a memoryless nonlinear controller results, which achieves near-optimal performance. The construction involves the solution of several finite linear programs and generalizes to the multirate case earlier work on Linear Time-Invariant (LTI) systems.


93B52 Feedback control
93C05 Linear systems in control theory
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