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Consider that a linear time-invariant (LTI) plant is given and that we wishto design a stabilizing controller for it. Admissible controllers are LTI andmust comply with a pre-selected sparsity pattern. The sparsity pattern isassumed to be quadratically invariant (QI) with respect to the plant, which,from prior results, guarantees that there is a convex parametrization of alladmissible stabilizing controllers provided that an initial admissible stablestabilizing controller is provided. This paper addresses the previouslyunsolved problem of determining necessary and sufficient conditions for theexistence of an admissible stabilizing controller. The main idea is to cast theexistence of such a controller as the feasibility of an exact model-matchingproblem with stability restrictions, which can be tackled using existingmethods. Furthermore, we show that, when it exists, the solution of themodel-matching problem can be used to compute an admissible stabilizingcontroller. This method also leads to a convex parametrization that may beviewed as an extension of Youla's classical approach so as to incorporatesparsity constraints. Applications of this parametrization on the design ofnorm-optimal controllers via convex methods are also explored. An illustrativeexample is provided, and a special case is discussed for which the exact modelmatching problem has a unique and easily computable solution.

Stabilizability and Norm-Optimal Control Design subject to Sparsity Constraints