Related papers: A Cyclic Small Phase Theorem
In this paper, we define the phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems whose frequency responses are (semi-)sectorial at all frequencies. The newly defined phase concept subsumes the…
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, we investigate the feedback stability of multiple-input multiple-output linear time-invariant systems with combined gain and phase information. To begin with, we explore the stability condition for a class of so-called easily…
In this paper, we introduce a definition of phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems, the frequency responses of which are cramped at all frequencies. This phase concept generalizes…
In this paper, we show that the small phase condition is both sufficient and necessary to ensure the feedback stability when the interconnected systems are symmetric. Such symmetric systems arise in diverse applications. The key lies in…
The stability of interconnected linear time-invariant systems using singular values and the small gain theorem has been studied for many decades. The methods of mu-analysis and synthesis has been extensively developed to provide robustness…
This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a…
It is known that the stability of a feedback interconnection of two linear time-invariant systems implies that the graphs of the open-loop systems are quadratically separated. This separation is defined by an object known as the multiplier.…
This paper proposes decentralized stability conditions for multi-converter systems based on the combination of the small gain theorem and the small phase theorem. Instead of directly computing the closed-loop dynamics, e.g., eigenvalues of…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
The cyclic feedback interconnection of $n$ subsystems is the basic building block of control theory. Many robust stability tools have been developed for this interconnection. Two notable examples are the small gain theorem and the Secant…
In this paper, we introduce an angle notion called the singular angle for nonlinear systems from an input-output perspective. The proposed system singular angle, based on the angle between $L_2$-signals, describes an upper bound for the…
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…
In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
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…
The increasing share of converter based resources in power systems calls for scalable methods to analyse stability without relying on exhaustive system wide simulations. Decentralized small gain and small-phase criteria have recently been…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…