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Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…
In this paper, we discuss the state feedback output regulation problem (SFRP) for infinite-dimensional linear control systems with infinite-dimensional exosystems. Under the polynomial stabilizability assumption, sufficient and necessary…
We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The…
We introduce a novel set of stability conditions for vacua with broken Lorentz symmetry. The first class of conditions require that the energy be minimized under small geometric deformations, which translates into requiring the positivity…
A system put in contact with a large heat bath normally thermalizes. This means that the state of the system approaches an equilibrium state, the latter depending only on macroscopic characteristics of the bath (e.g. temperature), but not…
A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…
Key properties of a physical system depend on whether it is gapped, i.e. whether its spectral gap has a positive lower bound that is independent of system size. In quantum information theory, the question of whether a system is gapped has…
We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis…
Decoherence represents a major obstacle towards realizing reliable quantum technologies. Identifying states that can be uphold against decoherence by purely coherent means, i.e., {\it stabilizable states}, for which the dissipation-induced…
We present a control scheme that is able to find and stabilize an unstable chaotic regime in a system with a large number of interacting particles. This allows us to track a high dimensional chaotic attractor through a bifurcation where it…
We consider optimization of linear stability of synchronized states between a pair of weakly coupled limit-cycle oscillators with cross coupling, where different components of state variables of the oscillators are allowed to interact. On…
We study local stabilization of nonlinear control systems under explicit gain constraints on the feedback law. Using a quantitative refinement of Brockett's openness condition, we introduce the notion of a maximal continuous openness rate…
While port-Hamiltonian descriptor systems are known to be stable and passive, they may not be asymptotically stable or strictly passive. Necessary and sufficient conditions are presented when these properties as well as the regularity and…
Assessing small-signal stability of power systems composed of thousands of interacting generators is a computationally challenging task. To reduce the computational burden, this paper introduces a novel condition to assess and certify…
A networked output feedback loop subject to packetized transmissions of the output signal is considered. Based on the small gain theorem, an easy-to-use stability criterion covering two important cases is presented. In the first case a…
Autonomous agents are often tasked with operating in an area where feedback is unavailable. Inspired by such applications, this paper develops a novel switched systems-based control method for uncertain nonlinear systems with temporary loss…
Emerging network scenarios require the development of solid large-scale situated systems. Unfortunately, the diffusion/aggregation computational processes therein often introduce a source of complexity that hampers predictability of the…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…