相关论文: Zames-Falb Multipliers: don't panic

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 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.…

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…

Lur'e systems are feedback interconnection of a linear time-invariant subsystem in the forward path and a memoryless nonlinear one in the feedback path, which have many physical representatives. In this paper, some classical theorems about…

Dynamic multipliers can be used to guarantee the stability of Lurye systems with slope-restricted nonlinearities, but give no guarantee that the closed-loop system has finite incremental gain. We show that multipliers guarantee the…

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…

Multipliers can be used to guarantee both the Lyapunov stability and input-output stability of Lurye systems with time-invariant memoryless slope-restricted nonlinearities. If a dynamic multiplier is used there is no guarantee the…

In this note it is shown that the famous multiplier absolute stability test of R. O'Shea, G. Zames and P. Falb is necessary and sufficient if the set of Lur'e interconnections is lifted to a Kronecker structure and an explicit method to…

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…

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…

A suite of input-to-state stability results are presented for a class of forced differential inclusions, so-called Lur'e inclusions. As a consequence, semi-global incremental input-to-state stability results for systems of forced Lur'e…

Lur'e-type nonlinear systems are virtually ubiquitous in applied control theory, which explains the great interest they have attracted throughout the years. The purpose of this paper is to propose conditions to assess incremental asymptotic…

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…

Incremental stability properties are considered for certain systems of forced, nonlinear differential equations with a particular positivity structure. An incremental stability estimate is derived for pairs of input/state/output…

This paper investigates the robustness of the Lur'e problem under positivity constraints, drawing on results from the positive Aizerman conjecture and robustness properties of Metzler matrices. Specifically, we consider a control system of…

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…

It is known that the stability of a feedback interconnection of two linear time-invariant systems implies that the graphs of the open-loop systems are quadratically separated. This separation is defined by an object known as the multiplier.…

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…

This paper is concerned with the absolute stability analysis of discrete-time feedback systems with slope-restricted nonlinearities. By employing static O'Shea-Zames-Falb multipliers in the framework of integral quadratic constraints, we…

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…