Stability tests for constrained linear systems

By M. C. Oliveira, Robert E. Skelton. 2001

710 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0ece154f45de4c960900d8298d618825952854f6

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In Control and Systems Engineering

In Mechanics of Materials

Citations in the corpus

ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs (2008, background): “Lemma 3 (Finsler’s Lemma, [29]) Let x 2 Rn; Q 2 Rn n (symmetric), and C 2 Rm n be such that rankðCÞ4n: The following statements are equivalent: (i) x0Qx > 0; 8Cx ¼ 0; x=0; (ii) ðC?”
Robust stability and stabilization of linear switched systems with dwell time (2010, methodology): “Applying the method of [ 10 ] we obtain the following.”
Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations (2007, methodology): “PD-LMI conditions which are equivalent to the conditions of Lemmas 1 (Hurwitz) and 2 (Schur) but present a larger number of decision variables can be formulated by using Finsler’s Lemma [25].”
Consensus Tracking of Multi-Agent Systems With Lipschitz-Type Node Dynamics and Switching Topologies (2014, methodology): “By using Finsler’s lemma [37] and the Schur complement lemma [35], one gets that there exist scalar and a matrix such that (22) holds if and only if there exist matrices and such that the following algebraic Riccati inequality holds:”
DELAY-DEPENDENT ROBUST STABILITY OF TIME DELAY SYSTEMS (2006, methodology): “In this, we follow methodologies based on Finsler lemma (Skelton et al. , 1998) known to be very effective in robust control (De Oliveira and Skelton, 2001) and that has been already used for the study of time delay systems in the delay independent case (Castelan et al. , 2003) and in the delay…”
Analytical and numerical Lyapunov functions for SISO linear control systems with first‐order reset elements (2011, methodology): “Then, by Finsler’s lemma [27], and performing a Schur complement, condition (15b) implies that (d(xT P0x)/dx)ẋ +(1/ )|y|2 − |w|2 <0 for all x = [ x1 0 ] with x1 ∈Rn−2.”
Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay (2015, neutral): “Lemma 5 [24]: Let ζ ∈ R, Φ = Φ (∈ Rn×n), and B ∈ Rm×n with rank(B) < n.”
On H∞ Performance Analysis for Continuous-Time Stochastic Systems with Polytopic Uncertainties (2005, methodology): “This is similar to the idea developed in [ 6 ], which employs Finsler’s lemma to incorporate the dynamic constraints into the stability conditions.”
Consensus of multi-agent systems with intrinsic nonlinear dynamics and sampled-data information (2011, neutral): “Lemma 3: [32]–[35] Suppose that x ∈ R, P = P ∈”