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We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide…
We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to…
This paper proposes dynamic stability and performance conditions for grid-connected inverter-based resources (IBRs). To this end, we extend the notion of steady-state droop coefficients to dynamic droop coefficients to capture the…
We will present a new general framework for robust and adaptive control that allows for distributed and scalable learning and control of large systems of interconnected linear subsystems. The control method is demonstrated for a linear…
In this paper, we examine both stability and sustainability of a network-based model of natural resource consumption. Stability is studied from a dynamical systems perspective, though we argue that sustainability is a fundamentally…
This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic…
The stability of a horizontal interface between two viscous fluids, one of which is conducting and the other is dielectric, acted upon by a vertical time-periodic electric field is considered. The two fluids are bounded by electrodes…
We address the conditions and design of controllers and observers for homogeneous networks of linear MIMO agents. We develop networked controllers and observers that ensure the stability of both the system state and the estimation error,…
This paper provides a framework to characterize the gain margin, phase margin, and maximum input delay margin of a linear time-invariant multi-agent system where the interaction topology is described by a graph with a directed spanning…
The power interactions of any component in electric energy systems with the rest of the system happen naturally, as governed by the energy conservation principles. There may, however, occur instances when the rate at which power gets…
In this paper, we establish the sufficient conditions guaranteeing global uniform exponential stability, or at least global asymptotic stability, of all solutions for nonlinear dynamical systems, also known as global incremental stability…
From the structural perspective, this paper investigates a new formulation of the concept of input-to-state stability (ISS), and based on this formulation, proposes a new stability analysis approach for a class of interconnected system. The…
This paper proposes a frequency-wise approach for stability analysis of multi-input, multi-output (MIMO) Linear Time-Invariant (LTI) feedback systems through Scaled Relative Graphs (SRGs). Unlike traditional methods, such as the Generalized…
This paper presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered.…
In a power grid with growing penetrations of renewable energy sources, inverters play a larger role in the dynamic interactions among network components. However, much is yet to be studied regarding inverter-dominated grid stability. This…
A major transition in modern power systems is the replacement of conventional generation units with renewable sources of energy. The latter results in lower rotational inertia which compromises the stability of the power system, as…
Stability analysis of a power network and its characterization (voltage or angle) is an important problem in the power system community. However, these problems are mostly studied using linearized models and participation factor analysis.…
A quantitative frequency-domain condition related to the exponential stabilizability for infinite-dimensional linear control systems is presented. It is proven that this condition is necessary and sufficient for the stabilizability of…
The small gain condition is sufficient for input-to-state stability (ISS) of interconnected systems. However, verification of the small gain condition requires large amount of computations in the case of a large size of the system. To…
As the amount of volatile, renewable energy sources in power distribution grids is increasing, the stability of the latter is a vital aspect for grid operators. Within the STABEEL project, the authors develop rules on how to parametrize the…