Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties

By Jamal Daafouz, J. Bernussou. Systems & control letters (Print), 2001

701 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/88ca9907893494a6f7ebb7c2cbb96bdbf3d6d0a9

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In Control and Systems Engineering

Citations in the corpus

Dynamic Output Feedback Control of Switched Linear Systems (2008, background): “The situation is even poorer in discrete time, where only a few works have appeared for the stabilization problem, see, e.g., [ 6 ], [7], [22], and [24].”
Gain scheduled control for discrete‐time systems depending on bounded rate parameters (2000, methodology): “In Reference [16] parameter dependent Lyapunov functions depending linearly on the parameter vector are used; however, the parameter rate of variation is not taken into account and the parameter bounds are given in terms of the vector 1-norm instead of the vector1-norm that we consider in this paper”
Interpolating model identification for SISO linear parameter-varying systems (2009, background): “There is a continuing effort to design LPV controllers that achieve higher performance while still guaranteeing stability for all possible parameter variations [6–17].”
Stability and stabilization of discrete time switched systems (2006, background): “It is interesting to mention that Theorem 1 also contains as a particular case the stability results of Daafouz and Bernussou (2001) which are less conservative than quadratic stability.”
A poly-quadratic stability based approach for linear switched systems (2002, methodology): “Using a necessary and su cient LMI based condition of polyquadratic stability, which has been proposed in Daafouz and Bernussou (2001), is it shown that a class of switched control problems can be easily solved.”
LMI-Based Control for Grid-Connected Converters With LCL Filters Under Uncertain Parameters (2014, background): “Note that if the conditions of Theorem 1 provide a feasible solution, it is guaranteed that the whole polytope (in closedloop) is robustly stable [41].”
Event‐triggered control for discrete‐time linear systems subject to bounded disturbance (2016, background): “The inequalities (29) and (30) [20, 21] are equivalent to”
Recent developments on the stability of systems with aperiodic sampling: An overview (2017, background): “One of the advantages of the polytopic embedding is the fact that it allows the use of parameter dependent Lyapunov functions [45,108,43] Ṽ (x, α) = xP (α)x, P (α) = Nv i=1 αiPi, which lead to refined stability conditions under a reasonable numerical complexity:”
Stability and stabilization of continuous descriptor systems: An LMI approach (2006, positive): “The PDL approach consists in expressing the Lyapunov matrix as a function of the uncertainty, and with the help of some slack additional variables, the approach yields a significant reduction of conservatism [1, 4, 6].”
Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays (2006, methodology): “The authors are with the Institut National Polytechnique de Lorraine, CRAN UMR 7039 CNRS, Nancy University, ENSEM, 54516 Vandoevre-Lès-Nancy, Cedex, France (e-mail: jamal.daafouz@ensem.inpl-nancy.fr). the results presented in [6] for switched uncertain systems with polytopic uncertainty.”