A new robust D-stability condition for real convex polytopic uncertainty

By Dimitri Peaucelle, D. Arzelier, Olivier Bachelier, J. Bernussou. 2000

743 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/035a7b02acea0f1b333b3d3a3f0eddf78e6a2cc8

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In Control and Systems Engineering

Citations in the corpus

Technical Communique: New dilated LMI characterizations for continuous-time multiobjective controller synthesis (2004, positive): “We next consider the dilated LMIs for the D-stability (Chilali & Gahinet, 1996; Peaucelle et al., 2000). Since the matrix A should be stable in Lemma 1, the regions D are restricted to those contained in the open left half-plane. In Theorems 3–5 given below, the LMIs in the condition (ii) are from C”
Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations (2007, background): “Note that the conditions of Theorem 4 can be easily extended to cope with any convex region in the complex plane following the lines depicted in [ 10 ] and [11].”
Robust Static Output Feedback Stabilization for Polytopic Uncertain Systems: Improving the Guaranteed Performance Bound (2003, background): “Some attempts have been made to solve this robust synthesis prob- lem (Geromel et al., 1991; Arzelier et al., 1993; de Oliveira et al., 1999; Peaucelle et al., 2000) in the state feedback case.”
Robust Observer Design for Unknown Inputs Takagi–Sugeno Models (2013, methodology): “This assumption, used in previous works [30], [34], [35], will be useful to derive design conditions.”
Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties (2012, background): “Note that it is well known that polytopic uncertainties exist in many real systems, and most uncertain control systems can be approximated by systems with polytopic uncertainties [11],[21],[24],[34].”
Robust stability functionals of state delayed systems with polytopic type uncertainties via parameterdependent Lyapunov functions (2002, methodology): “…2 Rn£n, N 2 Rn£n such that ¡W AM AdN M T A T ¡M ¡ MT ‡ U1 0 N T A T d 0 ¡NT ¡ N ‡ U2 2 6664 3 7775 < 0 …4† Remark 1: The equation with the form of (4) has appeared in Geromel et al. (1998, 1999), de Oliveira et al. (1999a, b), Bachelier et al. (1999), Peaucelle et al. (2000), Tuan et al. (2000).”
New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems (2005, background): “53, NO. 8, AUGUST 2005 punov functions can be found in [ 18 ].”
Stability of polytopes of matrices via affine parameter-dependent lyapunov functions : Asymptotically exact LMI conditions (2005, background): “Finally, note that Theorem 5 could easily be extended to cope with the stability analysis with respect to any convex region in the complex plane with an appropriate choice of Q(α), following the lines depicted in [6,10].”
DELAY-DEPENDENT ROBUST STABILITY OF TIME DELAY SYSTEMS (2006, background): “See for example (Peaucelle et al. , 2000) for details on this subject.”