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The paper explores a previously unknown connection relating the symmetry properties of an oscillator steady-state to the orthogonal representation of amplitude and phase variables in the small-signal regime. It is shown that only circuits…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
We here characterize the minimality of realization of arbitrary linear time-invariant dynamical systems through (i) intersection of the spectra of the realization matrix and of the corresponding state submatrix and (ii) moving the poles by…
In this study, we investigate the robust feedback stability problem for multiple-input-multiple-output linear time-invariant systems involving sectored-disk uncertainty, namely, dynamic uncertainty subject to simultaneous gain and phase…
Behavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized--and thus homogeneous--across the network,…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. Here we…
We consider a generalised non-commutative space-time in which non-commutativity is extended to all phase space variables. If strong enough, non-commutativity can affect stability of the system. We perform stability analysis on a couple of…
Feedback delay has been identified as a key ingredient in the quorum sensing synchronization of synthetic gene oscillators. While this influence has been evidenced at the theoretical level in a simplified system of degrade-and-fire…
The aim of this paper is to build up the theoretical framework for the recovery of sparse signals from the magnitude of the measurement. We first investigate the minimal number of measurements for the success of the recovery of sparse…
We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular…
The stability analysis of synchronization patterns on generalized network structures is of immense importance nowadays. In this article, we scrutinize the stability of intralayer synchronous state in temporal multilayer hypernetworks, where…
In this paper, we propose a definition of phase for a class of stable nonlinear systems called semi-sectorial systems, from an input-output perspective. The definition involves the Hilbert transform as a critical instrument to complexify…
In this paper, for linear time-invariant plants, where a collection of possible inputs and outputs are known a priori, we address the problem of determining the communication between outputs and inputs, i.e., information patterns, such that…
We present a new sufficient condition for finite-gain $L_2$ input-to-output stability of a networked system. The condition requires a matrix, that combines information on the $L_2$ gains of the sub-systems and their interconnections, to be…
The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to…
In this paper, we study stabilizability of discrete-time switched linear systems where the switching signal is considered as an arbitrary disturbance (and not a control variable). We characterize feedback stabilization via necessary and…
Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
In this paper, the incremental stability of interconnected switched nonlinear systems is discussed. The nature of switching considered is state-dependent. The incremental stability of the switched interconnected system is a stronger…