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We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from epidemiology to biochemistry. Here we analyze the eigenspectrum of the Jacobian matrices associated to a general…
Power systems naturally experience disturbances, some of which can damage equipment and disrupt consumers. It is important to quickly assess the likely consequences of credible disturbances and take preventive action, if necessary. However,…
This paper introduces a method for predicting the likely behaviors of continuous nonlinear systems in equilibrium in which the input values can vary. The method uses a parameterized equation model and a lower bound on the input joint…
In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…
This paper introduces an innovative method for ensuring global stability in a broad array of nonlinear systems. The novel approach enhances the traditional analysis based on Jacobian matrices by incorporating the Taylor series boundary…
Voltage instability is a major threat in power system operation. The growing presence of constant power loads significantly aggravates this issue, hence motivating the development of new analysis methods for both existence and stability of…
This study proposes a method for designing stabilizing suboptimal controllers for nonlinear stochastic systems. These systems include time-invariant stochastic parameters that represent uncertainty of dynamics, posing two key difficulties…
Typical measures of nonstabilizerness of a system of $N$ qubits require computing $4^N$ expectation values, one for each Pauli string in the Pauli group, over a state of dimension $2^N$. For permutationally invariant systems, this…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
Resilient systems are able to recover quickly and easily from disturbed system states that might result from hazardous events or malicious attacks. In this paper a novel resilience metric for linear time invariant systems is proposed: the…
The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in…
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or…
In this paper, we consider a stabilization problem of an uncertain system in a networked control setting. Due to the network, the measurements are quantized to finite-bit signals and may be randomly lost in the communication. We study…
We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown…
This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…
The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…