The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

Invariant theory has been a major subject of research in the 19th century. One of the highlights was Gordan’s famous theorem from 1868 showing that the invariants and covariants of binary forms have a finite basis. His method was constructive and led to explicit degree bounds for a system of generators (Jordan 1876/79). In 1890, Hilbert presented a very general finiteness result using completel...

In $d$ dimensions, the model for a massless $p$-form in curved space is known to be reducible gauge theory $p>1$, and therefore its covariant quantisation cannot carried out using standard Faddeev-Popov scheme. However, adding mass term also introducing Stueckelberg reformulation of resulting model, one ends up with an irreducible which can quantised \`a la Faddeev Popov. We derive compact expr...

This paper focuses on Kalman–Yakubovich–Popov lemma for multidimensional systems described by Roesser model that possibly includes both continuous and discrete dynamics. It is shown that, similarly to the standard 1-D case, this lemma can be studied through the lens of S-procedure. Furthermore, by virtue of this lemma, we will examine robust stability, bounded and positive realness of multidime...

To Philippe Biane, for his 55th birthday. CONTENTS 1. Introduction 2 1.1. Asymptotic representation theory 2 1.2. Connection with RMT 3 1.3. Biane-Perelomov-Popov quantization 4 1.4. The semiclassical limit 6 1.5. Mean values and asymptotic freeness 6 1.6. Proof strategy 8 1.7. Higher correlators and higher order freeness 9 2.

Andon Vassilev1, Jaco Vangronsveld2, Ivan Yordanov3 1Agricultural University of Plovdiv, Dept. Plant Physiology and Biochemistry, 12 Mendeleev St., 4000 Plovdiv, Bulgaria 2Environmental Biology, Center for Environmental Sciences, Limburgs Universitair Centrum, Universitaire Campus, B-3590 Diepenbeek, Belgium 3Acad. M. Popov Institute of Plant Physiology, Acad. G. Bonchev St., Bl.21, 1113, Sofia...

The action functional of the anisotropic Kantowski–Sachs cosmological model is turned into that of an ordinary gauge system. Then a global phase time is identified for the model by imposing canonical gauge conditions, and the quantum transition amplitude is obtained by means of the usual path integral procedure of Fadeev and Popov.