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We study a state estimation problem for a $2\times 2$ linear hyperbolic system on networks with eigenvalues with opposite signs. The system can be seen as a simplified model for gas flow through gas networks. For this system we construct an…
For a relative equilibrium of a symmetric simple mechanical system, if the Morse index of the corresponding amended potential is odd, whether the nullity is zero or not, it is linearly unstable. We also provide a sufficient condition for…
We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
We present a stability analysis of the classical ideal gas in a new theory of nonextensive statistics and use the theory to understand the phenomena of negative specific heat in some self-gravitating systems. The stability analysis is made…
Monitoring the long term voltage stability of the power grid is necessary to ensure its secure operation. This paper presents a new phasor based methodology that distinguishes between long term voltage stability caused by distribution…
We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
This paper derives distributed conditions that guarantee the system-wide stability for power systems with nonlinear and heterogeneous bus dynamics interconnected via power network. Our conditions require each bus dynamics should satisfy…
The quasi steady-state (QSS) model tries to reach a good compromise between accuracy and efficiency in long-term stability analysis. However, the QSS model is unable to provide correct approximations and stability assessment for the…
Most of the existing characterizations of the integral input-to-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This note provides…
We apply a duality method to prove an optimal stability theorem for the logarithmic Hardy-Littlewood-Sobolev inequality, and we apply it to the estimation of the rate of approach to equilibrium for the critical mass Keller-Segel system.
Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
With the increasing penetration of renewable energy sources, power system operation has to be adapted to ensure the system stability and security while considering the distinguished feature of the Power Electronics (PE) interfaced…
We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text).…
In this paper, a new methodology for stability assessment of a smart power system is proposed. The key to this assessment is an index called betweenness index which is based on ideas from complex network theory. The proposed betweenness…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
Passivity indices have been widely adopted to derive distributed stability certificates for power systems. Nevertheless, conventional passivity indices remain scalar-valued even for multi-input-multi-output (MIMO) systems, which can…
The progression of modern power systems towards converter-rich operations calls for new models and analytics in steady-state voltage stability assessment. The classic modeling assumption of the generators as stiff voltage sources no longer…