Stability of linear descriptor systems with delay: a Lyapunov-based approach

By Emilia M. Fridman. 2002

360 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/cd504efc0a426170dd3bfe61a0ae58fd9209250d

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In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Technical Communique: Effects of small delays on stability of singularly perturbed systems (2002, background): “LMI (20) guarantees for all h¿ 0 the asymptotic stability of the following slow (descriptor) system (Fridman, 2001):”
H∞-control of linear state-delay descriptor systems: an LMI approach (2002, methodology): “The latter guarantees robust stability with respect to small changes of delay [ 10 ].”
A delay‐dependent bounded real lemma for singular LPV systems with time‐variant delay (2012, background): “1 when L=0 involves fewer number of variables than those in [3, 6, 10–13, 15, 35], and has the same number of variables with those in [7, 8, 37].”
Small gain problem in coupled differential‐difference equations, time‐varying delays, and direct Lyapunov method (2011, background): “A number of other systems considered in the framework of singular systems and descriptor systems [16, 22] may also be considered as coupled differential-difference equations.”
Switched nonlinear singular systems with time‐delay: Stability analysis (2015, background): “As mentioned in [16], for ordinary singular time-delay systems with incompatible initial conditions, jump can occur in the algebraic variables .”
On the stability issues of switched singular time‐delay systems with slow switching based on average dwell‐time (2014, background): “E,Ap/ is regular and impulse-free, the system can still have finite discontinuities because of incompatible initial condition [11, 43].”
Robust stabilization for uncertain discrete singular systems with state delay (2008, background): “It can be viewed as a discrete counterpart of Lemma 1 of [10], which is used to demonstrate the stability for the continuous singular time-delay systems.”
Delay‐dependent robust H∞ controller synthesis for discrete singular delay systems (2011, methodology): “Based on the equivalent augmented model technique, sufficient conditions for delaydependent/delay-independent stability and for stability robustness with respect to small delays are given in [16].”
Technical Communique: Robust sampled-data stabilization of linear systems: an input delay approach (2004, neutral): “Note that the descriptor system (6) has no impulsive solutions since in (6b) y(t) is multiplied by the nonsingular matrix I ( Fridman, 2002 ).”
DELAY-DEPENDENT ROBUST STABILITY OF TIME DELAY SYSTEMS (2006, neutral): “(Niculescu et al. , 1995) 0.99 11 (Moon et al. , 2001) 4.3588 16 (Han, 2002) 4.4721 9 or 18 (Fridman, 2002) 4.47 27 (Xu and Lam, 2005) 4.4721 17 (Suplin et al. , 2004) 4 1 show that Theorem 1 gives similar results to papers using descriptor system approach and bounding techniques from (Lee et al. ,…”
DELAY-DEPENDENT STABILITY ANALYSIS OF LINEAR TIME DELAY SYSTEMS (2006, result): “• It is shown in (Gouaisbaut and Peaucelle, 2006) that for r = 1, the proposed result is equivalent to the main classical results of the literature (Han, 2002; Fridman , 2002; Xu and Lam, 2005; Suplin et al., 2004).”
Tutorial on Lyapunov-based methods for time-delay systems (2014, background): “The feasibility of (12) yields the following: (i) A and A7A1 are Hurwitz matrices, (ii) A (1)A1= ffiffiffiffiffiffiffiffiffiffi 1 d p is a Schur matrix, meaning that all its eigenvalues are inside the unit circle [8].”
Stability results for systems described by coupled retarded functional differential equations and functional difference equations (2007, background): “, u(t) ≡ 0) have been studied for the autonomous case in [1,12,15,21,23].”