H ∞ Approach to Virtual Actuators Design Dušan Krokavec, Anna Filasová, Vladimír Serbák and Pavol Liščinský Abstract The H ∞ approach to virtual actuators design, intended for linear continu- ous-time systems, is presented in the paper. Using the H ∞ principle, new condi- tions for virtual actuators design in P and PI structures are formulated in terms of linear matrix inequalities. Related to the static output control under influence of sin- gle actuator faults, an example is presented to highlight the benefit of the proposed framework. Keywords Linear systems ⋅ Virtual actuators ⋅ Fault tolerant control 1 Introduction To increase the reliability of systems, fault tolerant control (FTC) usually fix a system with faults so that it can continue its mission with certain limitations of functionality and quality. Considering this, the different approaches were studied in FTC design (see, e.g., [1, 3, 10, 15] and the references therein). The standard approach to control reconfiguration discards the nominal controller from the control loop and replace it with a new one so that its parameters are re-tuned in occurred fault conditions and, in dependency on the remaining set of sensors and actuators, to recover in a certain extent the performance of the fault-free control system [6, 9, 14, 16]. By contrast, D. Krokavec ( ✉ ) ⋅ A. Filasová ⋅ V. Serbák ⋅ P. Liščinský Faculty of Electrical Engineering and Informatics, Department of Cybernetics and Artificial Intelligence, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia e-mail: dusan.krokavec@tuke.sk URL: http://web.tuke.sk/kkui A. Filasová e-mail: anna.filasova@tuke.sk V. Serbák e-mail: vladimir.serbak@tuke.sk P. Liščinský e-mail: pavol.liscinsky@tuke.sk © Springer International Publishing Switzerland 2016 Z. Kowalczuk (ed.), Advanced and Intelligent Computations in Diagnosis and Control, Advances in Intelligent Systems and Computing 386, DOI 10.1007/978-3-319-23180-8_15 209