arXiv subjects

Eder Baron-Prada

Publications and source records attributed to Eder Baron-Prada.

8 recordsLinked to original sources

arXiv2026

Scaled Graph Containment for Feedback Stability: Soft-Hard Equivalence and Conic Regions

Scaled graphs (SGs) offer a geometric framework for feedback stability analysis. This paper develops containment conditions for SGs within multiplier-defined regions, addressing both circular and conic geometries. For circular regions, we show that soft and hard SG containment are equivalent whenever the associated multiplier is positive-negative. This enables hard stability certification from soft computations alone, bypassing both the positive semidefinite storage constraint and the homotopy condition of existing methods. Numerical experiments on systems with up to 300 states demonstrate computational savings of 15-44 % for the circular containment framework. We further characterize which conic regions are hyperbolically convex, a condition our frequency-domain certificate requires, and demonstrate that such regions provide tighter SG bounds than circles whenever the operator SG is nonsymmetric.

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arXiv2026

On the Impact of Operating Points on Small-Signal Stability: Decentralized Stability Sets via Scaled Relative Graphs

This paper presents a decentralized frequency-domain framework to characterize the influence of the operating point on the small-signal stability of converter-dominated power systems. The approach builds on Scaled Relative Graph (SRG) analysis, extended here to address Linear Parameter-Varying (LPV) systems. By exploiting the affine dependence of converter admittances on their steady-state operating points, the centralized small-signal stability assessment of the grid is decomposed into decentralized, frequency-wise geometric tests. Each converter can independently evaluate its feasible stability region, expressed as a set of linear inequalities in its parameter space. The framework provides closed-form geometric characterizations applicable to both grid-following (GFL) and grid-forming (GFM) converters, and validation results confirm its effectiveness.

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arXiv2026

Stability Analysis of Power-Electronics-Dominated Grids Using Scaled Relative Graphs

This paper presents a novel approach to stability analysis for grid-connected converters utilizing Scaled Relative Graphs (SRG). Our method effectively decouples grid and converter dynamics, thereby establishing a comprehensive and efficient framework for evaluating closed-loop stability. Our analysis accommodates both linear and non-linear loads, enhancing its practical applicability. Furthermore, we demonstrate that our stability assessment remains unaffected by angular variations resulting from dq-frame transformations, significantly increasing the method's robustness and versatility. The effectiveness of our approach is validated in several simulation case studies, which illustrate its broad applicability in modern power systems.

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arXiv2025

Computing the Hard Scaled Relative Graph of LTI Systems

Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of nonlinear systems, where Linear Time-Invariant (LTI) systems are the fundamental building block. To analyze feedback loops with unstable LTI components, the hard SRG is required, since it aptly captures the input/output behavior on the extended $L_2$ space. In this paper, we develop a systematic computational method to exactly compute the hard SRG of LTI systems, which may be unstable and contain integrators. We also study its connection to the Nyquist criterion, including the multivariable case, and demonstrate our method on several examples.

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arXiv2025

Mixed Small Gain and Phase Theorem: A new view using Scale Relative Graphs

We introduce a novel approach to feedback stability analysis for linear time-invariant (LTI) systems, overcoming the limitations of the sectoriality assumption in the small phase theorem. While phase analysis for single-input single-output (SISO) systems is well-established, multi-input multi-output (MIMO) systems lack a comprehensive phase analysis until recent advances introduced with the small-phase theorem. A limitation of the small-phase theorem is the sectorial condition, which states that an operator's eigenvalues must lie within a specified angle sector of the complex plane. We propose a framework based on Scaled Relative Graphs (SRGs) to remove this assumption. We derive two main results: a graphical set-based stability condition using SRGs and a small-phase theorem with no sectorial assumption. These results broaden the scope of phase analysis and feedback stability for MIMO systems.

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arXiv2025

Stability results for MIMO LTI systems via Scaled Relative Graphs

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 Nyquist Criterion (GNC), which relies on a coupled analysis that requires the multiplication of models, our approach enables the evaluation of system stability in a decoupled fashion, system by system, each of which is represented by its SRG (or an over-approximation thereof), and it provides an intuitive, visual representation of system behavior. Our results provide conditions for certifying the stability of stable and square MIMO LTI systems connected in closed loop.

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arXiv2022

From Observability to Observer Realization: A path via elementary block-diagram manipulations

Introductory state-space linear control courses focus on linear, time-invariant systems and spend intense efforts by introducing system realizations that allow the student to grasp fundamental concepts, among which controllability, observability, and controller and observer design. This note describes a graphical mechanism to transform a system expressed in observability form into its observer form based on elementary block diagram manipulations, a technique whose pedagogical usefulness tends to be overlooked. Given the well-known duality principle in linear systems with respect to controllability and observability, the proposed graphical mechanism is applicable to transform from controllability to controller realization.

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arXiv2018

A Method for Distributed Transactive Control in Power Systems based on the Projected Consensus Algorithm

The shift of power systems toward a smarter grid has brought devices such as distributed generators and smart loads with an increase of the operational challenges for the system operator. These challenges are related to the real-time implementation as well as control and stability issues. We present a distributed transactive control strategy, based on the projected consensus algorithm, to operate the distributed energy resources and smart loads of a power system toward optimal social welfare. We consider two types of agents: Generators, and smart loads. Each agent iteratively optimizes its local utility function based on local information obtained from its neighbors and global information obtained through the network of agents. We show convergence analysis and numerical results for the proposed method.

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