Related papers: Noncausal FIR Zames-Falb Multiplier Search for Exp…
We analyze the performance of source-seeking dynamics involving either a single vehicle or multiple flocking-vehicles embedded in an underlying strongly convex scalar field with gradient based forcing terms. For multiple vehicles under…
In this paper we develop and analyse convex searches for Zames--Falb multipliers. We present two different approaches: Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) multipliers. The set of FIR multipliers is complete in…
In this paper, we analyze the stability of feedback interconnections of a linear time-invariant system with a neural network nonlinearity in discrete time. Our analysis is based on abstracting neural networks using integral quadratic…
This paper analyzes internal stability of a discrete-time feedback system with a ReLU nonlinearity. This feedback system is motivated by recurrent neural networks. We first review existing static quadratic constraints (QCs) for…
The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…
The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…
Zames-Falb multipliers are mathematical constructs which can be used to prove stability of so-called Lur'e systems: systems that consist of a feedback interconnection of a linear element and a static nonlinear element. The main advantage of…
This paper presents a new dynamic integral quadratic constraint (IQC) for the repeated Rectified Linear Unit (ReLU). These dynamic IQCs can be used to analyze stability and induced $\ell_2$-gain performance of discrete-time, recurrent…
We present a new approach to verifying contraction and $L_2$-gain of uncertain nonlinear systems, extending the well-known method of integral quadratic constraints. The uncertain system consists of a feedback interconnection of a nonlinear…
We study cooperative control dynamics with gradient based forcing terms. As a specific example, we focus on source-seeking dynamics with vehicles embedded in an unknown scalar field with a subset of agents having gradient information. As…
This paper develops a robust control synthesis method for uncertain linear systems with input saturation in the framework of integral quadratic constraints (IQCs). The system is reformulated as a linear fractional representation (LFR) that…
This study investigates the absolute stability criteria based on the framework of integral quadratic constraint (IQC) for feedback systems with slope-restricted nonlinearities. In existing works, well-known absolute stability certificates…
This paper analyzes the robust feedback stability of a single-input-single-output stable linear time-invariant (LTI) system against four different classes of nonlinear systems using the Zames-Falb multipliers. The contribution is fourfold.…
We propose novel time-domain dynamic integral quadratic constraints with a terminal cost for exponentially weighted slope-restricted gradients of not necessarily convex functions. This extends recent results for subdifferentials of convex…
Conditions for input-output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs).…
This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…
We consider a sequence of Hawkes processes whose excitation measures may depend on the generation, and study its scaling limits in the near-unstable limiting regime. The limiting random measures, characterized via a nonlinear convolutional…
We consider Lurye (sometimes written Lur'e) systems whose nonlinear operator is characterised by a possibly multivalued nonlinearity that is bounded above and below by monotone functions. Stability can be established using a sub-class of…
This paper presents a unified matrix factorization framework for classical and robust clustering. We begin by revisiting the well-known equivalence between crisp k-means clustering and matrix factorization, following and rigorously…
Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter…