Solution to negative-imaginary control problem for uncertain LTI systems with multi-objective performance

• Autores: Parijat Bhowmick, Sourav Patra
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 112, 2020
• Idioma: inglés
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• Resumen

  • This paper addresses the problem of dynamic output feedback controller synthesis in LMI framework for LTI generalized plants with negative-imaginary uncertainties. The proposed technique transforms the controller synthesized nominal closed-loop system into a strongly strict negative-imaginary system and exploits the DC loop gain condition pertaining to negative-imaginary theory to establish internal stability in presence of negative-imaginary uncertainties. Apart from making the closed-loop system robustly stable, the designed output feedback controller also facilitates multi-objective performance of the closed-loop system such as minimizing the H2 and H∞ norms, reducing the peak overshoot, increasing the decay rate, optimizing the settling time, etc. Illustrative examples have been studied to demonstrate the usefulness of the proposed control scheme. A thorough μ-analysis subjected to ‘mixed’ two-block perturbations is included in the examples to show that the designed controller can also facilitate a certain level of robust H∞ performance in presence of stable NI/SNI uncertainties.