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An LMI solution to the robust synthesis problem for multi-rate sampled-data systems. (English) Zbl 1031.93121
The paper deals with a solution to the multi-rate sampled-data \(H_\infty\) synthesis problem without unnecessary constraints on the original system data. Using the method developed by the authors [IEEE Trans. Autom. Control 44, 1486-1497 (1999; Zbl 1136.93321)], the multi-rate sampled-data problem is converted into an equivalent discrete-time, time-varying synthesis problem. One of the main advantages of this approach is that the solution is developed via a convex optimization problem expressed in the form of linear operator inequalities. For synthesis problems with rational sampling rates, the solutions are expressed in terms of finite-dimensional linear matrix inequalities, for which standard numerical solvers are available.

MSC:
93C57 Sampled-data control/observation systems
93B36 \(H^\infty\)-control
93B50 Synthesis problems
15A39 Linear inequalities of matrices
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