Related papers: Robust Exponential Stability and Invariance Guaran…
We develop a novel convex parametrization of integral quadratic constraints with a terminal cost for subdifferentials of convex functions, involving general O'Shea-Zames-Falb multipliers. We show the benefit of our results for the reduction…
In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections…
We develop phase limitations for the discrete-time Zames-Falb multipliers based on the separation theorem for Banach spaces. By contrast with their continuous-time counterparts they lead to numerically efficient results that can be computed…
This paper considers the robust stability of a discrete-time Lurye system consisting of the feedback interconnection between a linear system and a bounded and monotone nonlinearity. It has been conjectured that the existence of a suitable…
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…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
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…
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…
We study robustness properties of some iterative gradient-based methods for strongly convex functions, as well as for the larger class of functions with sector-bounded gradients, under a relative error model. Proofs of the corresponding…
Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…
Phase limitations of both continuous-time and discrete-time Zames-Falb multipliers and their relation with the Kalman conjecture are analysed. A phase limitation for continuous-time multipliers given by Megretski is generalised and its…
We show how to compose robust stability tests for uncertain systems modeled as linear fractional representations and affected by various types of dynamic uncertainties. Our results are formulated in terms of linear matrix inequalities and…
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 convex optimization-based framework for synthesizing time-varying controlled invariant funnels and associated feedback control around a given nominal trajectory for nonlinear systems subject to bounded disturbances.…
We propose a computationally tractable method for the identification of stable canonical discrete-time rational transfer function models, using frequency domain data. The problem is formulated as a global non-convex optimization problem…
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…
Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD)…
In the existing literature, there are two approaches to estimate tighter bounds of the exponential convergence rate of stable Lure systems. On one hand, the classical integral quadratic constraint (IQC) framework can be applied under…
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.…
In the setting of continuum elasticity martensitic phase transformations are characterized by a non-convex free energy density function that possesses multiple wells in strain space and includes higher-order gradient terms for…