We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

In the domain of passivity theory, there were major contributions in last decade, most recent notion being so-called Krasovskii passivity. This framework offers possibility designing a controller which ensures resulting closed-loop system. The current paper proposes solution to design parameters passivity-based controllers (K-PBCs) order ensure small sensitivity systems. As such, after initial ...

Motivated by current sharing in power networks, we consider a class of output consensus (also called agreement) problems for nonlinear systems, where the value is determined external disturbances, e.g., demand. This problem solved simple distributed feedback controller if system either Krasovskii or shifted passive, which only essential requirement. The effectiveness proposed shown simulation o...

In the talk we present a survey of the current state of art in the area of quadratic functionals with prescribed time derivatives. The …rst contribution dedicated to the topic was that by Yu.M. Repin [5]. In this seminal contribution a quadratic functional of a general form was suggested. The time derivative of the functional has been computed, and then, equating the derivative to the prescribe...

The input-to-state stability of time-invariant systems described by coupled differential and difference equationswithmultiple noncommensurate and distributed time delays is investigated in this paper. Such equations include neutral functional differential equations in Hale’s form (which model, for instance, partial element equivalent circuits) and describe lossless propagation phenomena occurri...

Time–delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time–varying delay signals and we propose one approach to the control design of such systems, which is based on the construction of symbolic models. Symbolic models are a...

This paper is aimed at application of the passification based adaptive control to decentralized synchronization of dynamical networks. We consider Lurie type systems with hyper-minimum-phase linear parts and two types of nonlinearities: Lipschitz and matched. The network is assumed to have both instant and delayed time-varying interconnections. Agent model may also include delays. Based on the ...

We examine the stability problem for delayed neutral-type neural networks (NNs) with interval time-varying delay signals under the effects of leakage term by constructing a suitable Lyapunov–Krasovskii functionals (LKFs) with the tripleand four-integral terms and using the famous Jensen inequality, Wirtinger single integral inequality (WSII), and Wirtinger double integral inequality (WDII), com...

This special issue on “System Theory and Delay” is dedicated to Vladimir Kharitonov the occasion of his 70th birthday, in recognition academic leadership this field research. His work systems with delays (a topic that has captured interest since early years research) reached maturity well-known contributions Lyapunov–Krasovskii functionals, delay Lyapunov matrices, prediction-based control. als...

This paper investigates input-to-state stability (ISS) and integral input-to-state stability (iISS) of impulsive and switching hybrid systems with time-delay, using the method of multiple Lyapunov–Krasovskii functionals. It is shown that, even if all the subsystems governing the continuous dynamics, in the absence of impulses, are not ISS/iISS, impulses can successfully stabilize the system in ...