Sufficient Dilated LMI Conditions for Static Output Feedback Robust Stabilization of Linear Continuous-Time Systems

New sufficient dilated linear matrix inequality (LMI) conditions for the ∞ static output feedback control problem of linear continuous-time systems with no uncertainty are proposed. The used technique easily and successfully extends to systems with polytopic uncertainties, by means of parameter-dependent Lyapunov functions (PDLFs). In order to reduce the conservatism existing in early standard LMI methods, auxiliary slack variables with even more relaxed structure are employed. It is shown that these slack variables provide additional flexibility to the solution. It is also shown, in this paper, that the proposed dilated LMI-based conditions always encompass the standard LMI-based ones. Numerical examples are given to illustrate the merits of the proposed method

New Dilated LMI Characterization for the Multiobjective Full-Order Dynamic Output Feedback Synthesis Problem

<p/> <p>This paper introduces new dilated LMI conditions for continuous-time linear systems which not only characterize stability and <inline-formula> <graphic file="1029-242X-2010-608374-i1.gif"/></inline-formula> performance specifications, but also, <inline-formula> <graphic file="1029-242X-2010-608374-i2.gif"/></inline-formula> performance specifications. These new conditions offer, in addition to new analysis tools, synthesis procedures that have the advantages of keeping the controller parameters independent of the Lyapunov matrix and offering supplementary degrees of freedom. The impact of such advantages is great on the multiobjective full-order dynamic output feedback control problem as the obtained dilated LMI conditions always encompass the standard ones. It follows that much less conservatism is possible in comparison to the currently used standard LMI based synthesis procedures. A numerical simulation, based on an empirically abridged search procedure, is presented and shows the advantage of the proposed synthesis methods.</p