Related papers: Transient dynamics under structured perturbations:…
Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of…
We consider the additive superimposition of an extensive number of independent Euclidean Random Matrices in the high-density regime. The resolvent is computed with techniques from free probability theory, as well as with the replica method…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
In the analysis and control of discrete-time linear time-invariant systems, the spectral radius of the system state matrix plays an essential role. Usually, it is assumed that system matrices are known, from which the spectral radius can be…
This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and…
We propose a novel data-dependent structured gradient regularizer to increase the robustness of neural networks vis-a-vis adversarial perturbations. Our regularizer can be derived as a controlled approximation from first principles,…
We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…
We consider $n\times n$ non-Hermitian random matrices with independent entries and a variance profile, as well as an additive deterministic diagonal deformation. We show that their empirical eigenvalue distribution converges to a limiting…
Recent works have established the utility of sparsity-promoting norms for extracting spatially-localized instability mechanisms in fluid flows, with possible implications for flow control. However, these prior works have focused on linear…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on…
Existing methods to determine the stability of a power system to small perturbations are based on eigenvalue analysis and focus on the asymptotic (long-term) behavior of the power grid. During the preasymptotic (short-term) transient,…
We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the ergodic constant of a risk-sensitive control problem, or of…
We consider nonlinear delay differential and renewal equations with infinite delay. We extend the work of Gyllenberg et al, Appl. Math. Comput. (2018) by introducing a unifying abstract framework, and derive a finite-dimensional…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…
Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them…
We develop a singular pseudodifferential calculus. The symbols that we consider do not satisfy the standard decay with respect to the frequency variables. We thus adopt a strategy based on the Calderon-Vaillancourt Theorem. The remainders…
The sensitivity of eigenvalues of structured matrices under general or structured perturbations of the matrix entries has been thoroughly studied in the literature. Error bounds are available and the pseudospectrum can be computed to gain…
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…