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The synchronization problem over the special orthogonal group $SO(d)$ consists of estimating a set of unknown rotations $R_1,R_2,...,R_n$ from noisy measurements of a subset of their pairwise ratios $R_{i}^{-1}R_{j}$. The problem has found…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
The PID controller remains the most widely adopted control architecture, with groundbreaking success across extensive implications. However, optimal parameter tuning for PID controller remains a critical challenge. Existing theories…
A robust-to-dynamics optimization (RDO) problem is an optimization problem specified by two pieces of input: (i) a mathematical program (an objective function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ and a feasible set…
This paper addresses the real structured controllability, stabilizability, and stability radii (RSCR, RSSZR, and RSSR, respectively) of linear systems, which involve determining the distance (in terms of matrix norms) between a (possibly…
A new method for the stability assessment of inverter-based microgrids is presented in this paper. Directly determining stability boundaries by searching the multidimensional space of inverters' droop gains is a computationally prohibitive…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…
In this paper we address the question of robustness of critical bit rates for the stabilization of networked control systems over digital communication channels. For a deterministic nonlinear system, the smallest bit rate above which…
Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…
As the growing penetration of inverter-based resources (IBRs) in modern power systems, the system strength is decreasing. Due to the inherent difference in short-circuit capacity contributions of synchronous generators and inverters, the…
The robust stability problem involves designing a controlled system which remains stable in the presence of modeling uncertainty. In this context, results known as small gain theorems are used to quantify the maximum amount of uncertainty…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
Explicit solutions to optimal control problems are rarely obtainable. Of particular interest are the explicit solutions derived for minimax problems, providing a framework to address adversarial conditions and uncertainty. This work…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…
Stability is an important aspect of a classification procedure because unstable predictions can potentially reduce users' trust in a classification system and also harm the reproducibility of scientific conclusions. The major goal of our…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
The proportional-integral-derivative (PID) controller and its variants are widely used in control engineering, but they often rely on linearization around equilibrium points and empirical parameter tuning, making them ineffective for…
We recapitulate the notion of phase change rate maximization and demonstrate the usefulness of its solution on analyzing the robust instability of a cyclic network of multi-agent systems subject to a homogenous multiplicative perturbation.…
In this paper we consider a possibility of stabilizing very fast electromagnetic interactions between Inverter Based Resources (IBRs), known as the Control Induced System Stability problems. We propose that when these oscillatory…