Related papers: Mixed Small Gain and Phase Theorem: A new view usi…
This article presents input-output stability analysis of nonlinear feedback systems based on the notion of soft and hard scaled relative graphs (SRGs). The soft and hard SRGs acknowledge the distinction between incremental positivity and…
Oscillatory behavior is a key property of many biological systems. The Small-Gain Theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a…
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…
In this paper, we show that the small phase condition is both sufficient and necessary to ensure the feedback stability when the interconnected systems are symmetric. Such symmetric systems arise in diverse applications. The key lies in…
Scaled Relative Graphs (SRGs) provide a novel graphical frequency-domain method for the analysis of Nonlinear (NL) systems. In this paper, we restrict the SRG to particular input spaces to compute frequency-dependent incremental gain bounds…
Scaled graphs offer a graphical tool for analysis of nonlinear feedback systems. Although recently substantial progress has been made in scaled graph analysis, at present their use in multivariable feedback systems is limited by…
This paper proposes a systematic framework to assess the small-signal stability of power systems with high shares of grid-following inverter-based resources (IBRs) under varying controller parameters and operating conditions. Stability…
We introduce a generalization of the scaled relative graph (SRG) to pairs of operators, enabling the visualization of their relative incremental properties. This novel SRG framework provides the geometric counterpart for the study of…
In this paper, the feedback stabilization of a linear time-invariant (LTI) multiple-input multiple-output (MIMO) system cascaded by a linear stochastic system is studied in the mean-square sense. Here, the linear stochastic system can model…
Scaled Relative Graphs (SRGs) provide an intuitive graphical frequency-domain method for the analysis of Nonlinear (NL) systems, generalizing the Nyquist diagram. In this paper, we develop a method for computing $L_2$-gain bounds for Lur'e…
This work encompasses Rate-Splitting (RS), providing significant benefits in multi-user settings in the context of huge degrees of freedom promised by massive Multiple-Input Multiple-Output (MIMO). However, the requirement of massive MIMO…
This paper proposes decentralized stability conditions for multi-converter systems based on the combination of the small gain theorem and the small phase theorem. Instead of directly computing the closed-loop dynamics, e.g., eigenvalues of…
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)…
Scaled relative graphs were recently introduced to analyze the convergence of optimization algorithms using two dimensional Euclidean geometry. In this paper, we connect scaled relative graphs to the classical theory of input/output…
This paper presents a unified mathematical paradigm, based on stochastic geometry, for downlink cellular networks with multiple-input-multiple-output (MIMO) base stations (BSs). The developed paradigm accounts for signal retransmission upon…
Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a…
The output impedance matrices of three-phase grid-connected voltage source converters (VSCs) are widely used in power system stability analysis. Regardless of how the impedance is modeled, there always exist coupling terms in the impedance…
Motivated by a paradigm shift towards a hyper-connected world, we develop a computationally tractable small-gain theorem for a network of infinitely many systems, termed as infinite networks. The proposed small-gain theorem addresses…
The scaled graph has been introduced recently as a nonlinear extension of the classical Nyquist plot for linear time-invariant systems. In this paper, we introduce a modified definition for the scaled graph, termed the signed scaled graph…
A unified structural framework is presented for model-based fault diagnosis that explicitly incorporates both fault locations and constraints imposed by the residual generation methodology. Building on the concepts of proper and minimal…