https://hal.inria.fr/hal-00793576Montagner, VinÃcius F.VinÃcius F.MontagnerUNIPAMPA - Federal University of PampaOliveira, RicardoRicardoOliveiraUNICAMP - Universidade Estadual de Campinas = University of CampinasPeres, Pedro L.D.Pedro L.D.PeresUNICAMP - Universidade Estadual de Campinas = University of CampinasBliman, Pierre-AlexandrePierre-AlexandreBlimanSISYPHE - SIgnals and SYstems in PHysiology & Engineering - Inria Paris-Rocquencourt - Inria - Institut National de Recherche en Informatique et en AutomatiqueStability analysis and gain-scheduled state feedback control for continuous-time systems with bounded parameter variationsHAL CCSD2009[INFO] Computer Science [cs]Briot, Brigitte2013-02-22 15:37:352022-08-05 11:52:042013-02-22 15:37:35enJournal articles10.1080/002071708024037501The problems of robust stability analysis and state feedback control based on gain-scheduling for continuous-time systems with time-varying parameters that have bounded rates of variation and lie inside a polytope are addressed in this article. With respect to previous results in the literature, two main contributions of the article are: (i) the robust stability analysis conditions are less conservative and demand less computational effort than the existing ones; (ii) the conditions can be extended to cope with the problem of control design for this class of system. Parameter-dependent linear matrix inequality (LMI) conditions are given for the existence of a parameter-dependent Lyapunov function quadratic in the state and homogeneous polynomially of arbitrary degree in the parameter assuring robust stability. Two convex procedures based on LMIs exhibiting distinct complexities are proposed to solve the problem of robust stability. An extension to deal with the computation of a stabilising parameter-dependent state feedback gain for this class of time-varying systems is also provided, as a sequence of LMIs of increasing precision. Examples illustrate the results, including comparisons with other techniques from the literature.