The paper is concerned with the fault detection filter design requirements that relax the existing conditions reported in the previous literature by adapting the unitary system principle in approximation of fault detection filter transfer function matrix for continuous-time linear MIMO systems. Conditions for the existence of a unitary construction are presented under which the fault detection filter with a unitary transfer function can be designed to provide high residual signals sensitivity with respect to faults. Otherwise, reflecting the emplacement of singular values in unitary construction principle, an associated structure of linear matrix inequalities with built-in constraints is outlined to design the fault detection filter only with a Hurwitz transfer function. All proposed design conditions are verified by the numerical illustrative examples.

The paper deals with the problem of the output feedback stabilization of the continuous-time nonlinear systems using the biproper Takagi-Sugeno dynamic output controller of order equal to the plant model order. The design procedure is based on the solution of the set of linear matrix inequalities and one matrix equality and ensures the closed-loop quadratic stability using Lyapunov approach, aggregating the fuzzy interactions among the subsystems. The numerical examples are given to illustrate the design procedure and the relevance of the method, as well as to validate the performances of the proposed approach.

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The H ∞ norm approach to virtual actuators design, intended to Takagi-Sugeno fuzzy continuous-time systems, is presented in the paper. Using the second Ljapunov method, the design conditions are formulated in terms of linear matrix inequalities in adapted bounded real lemma structures. Related to the static output controller, and for systems under influence of single actuator faults, the design steps are revealed for a three-tank system plant.

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