Infinite gain margin, contraction and optimality: An LMI-based design

On Contraction Analysis of Switched Systems With Mixed Contracting-Noncontracting Modes via Mode-Dependent Average Dwell Time

“…( 18) holds. By Theorem 4.4, it implies that (1) is contracting for any switching signals satisfying (20).…”

“…Hence Γp = 1 0 0 0 , which is less than γ 2 I. In addition, if ▽xgp(x, t) is a symmetric matrix, such inequality reduces to the incremental monotonic condition present in [20], or the uniformly Lipschitz smooth condition introduced in [21].…”

“…Then the switched nonlinear system (1) is contracting for any MDADT/MDALT switching signals satisfying (20), and which have mode dependent dwell time τ dp > 0.…”

A Sufficient Condition for $k$-Contraction of the Series Connection of Two Systems

“…Euclidean norms under differential sector bound or monotonicity assumptions on the nonlinearity (see also (Bullo, 2022, Theorem 3.24) for a similar condition under different assumptions), and use it to design controllers which guarantee contraction of the closed-loop system. This design method was then revisited by Giaccagli et al (2022) where it was shown that the designed controllers yield a closed-loop system with infinite gain margin. Proskurnikov et al (2022) provide a sufficient condition for contraction w.r.t.…”

Contraction analysis of nonlinear systems and its application

“…As one of the stability analysis methods that has received a growing interest lately, contraction analysis is concerned with the relative trajectories of a systems than to a particular attractor equilibrium point in standard Lyapunov stability analysis. There are many different methods to analyze the contractivity of nonswitched systems in literature, such as [4,6,7,12,27,30,40,55,65,74] among many others. In [55], the contraction property can be guaranteed if the largest eigenvalue of the symmetric part of the associated variational systems matrix (which is loosely termed as the Jacobian) is uniformly strictly negative.…”