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This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
Inhibitory circuits of relaxation oscillators are often-used models for the dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three reciprocally coupled…
We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of…
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and…
Control Co-Design (CCD) considers the coupled effects of both the plant and control parameters to optimize a system's closed-loop transient performance during the design stage. This paper presents a new method for CCD with guarantees on…
Classical and quantum dynamics of a harmonic oscillator in a monochromatic wave is studied in the exact resonance and near resonance cases. This model describes, in particular, a dynamics of a cold ion trapped in a linear ion trap and…
In this paper, a novel online, output-feedback, critic-only, model-based reinforcement learning framework is developed for safety-critical control systems operating in complex environments. The developed framework ensures system stability…
This paper investigates the stability of switched linear systems whose switching signal is modeled as a stochastic process called a regenerative process. We show that the mean stability of such a switched system is characterized by the…
Experiments have shown that flow in compliant microchannels can become unstable at a much lower Reynolds number than the corresponding flow in a rigid conduit. Therefore, it has been suggested that the wall's elastic compliance can be…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The 1-D Two-Fluid Model (TFM) promises a powerful and computationally cheap platform for simulating multi-fluid flow phenomena. However, runaway Kelvin-Helmholtz instabilities plagued previous approaches, necessitating aphysical…
It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term…
We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to…
Control-based continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The basic idea is to apply the method of numerical continuation to a feedback-controlled physical experiment. Since in an…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
A new type of nonlinear time series analysis is introduced, based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit…
In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of…
Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of…
With the increasing penetration of Inverter-Based Resources (IBRs), power system stability constraints must be incorporated into the operational framework, transforming it into stability-constrained optimization. Currently, there exist…
Recent research has shown that supervised learning can be an effective tool for designing optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of these neural network (NN) controllers is still not…