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A polynomial eigenvalue test for checking DLMI constraints
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DOI：10.1016/j.automatica.2022.110729.png)
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Abstract
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In order to obtain an optimization problem with a finite number of variables and constraints, Differential Linear Matrix Inequalities (DLMIs) are usually recast into the form of a system of LMIs. To this end, a typical approach consists in parameterizing the solution as a linear combination of known functions, with weights to be optimized. The constraints are then imposed on a finite set of discrete time points. This technical communique is concerned with the problem of checking whether a matrix polynomial solution obtained in this manner satisfies the original DLMI constraints. To this end, a novel test based on the concept of polynomial eigenvalues is presented. The proposed test is illustrated through a numerical example based on the H-infinity synthesis of a sampled-data controller. (c) 2022 Elsevier Ltd. All rights reserved.
Keywords:
Differential Linear Matrix Inequalities
Polynomial eigenvalues
Sampled-data control
Optimization-based controller synthesis
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5.9
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1.2W
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5.2W
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