Abstract
ABSTRACT Incremental stability and convergence properties for forced, infinite-dimensional, discrete-time Lur'e systems are addressed. Lur'e systems have a linear and nonlinear component and arise as the feedback interconnection of a linear control system and a static nonlinearity. Discrete-time Lur'e systems arise in, for example, sampled-data control and integro-difference models. We provide conditions, reminiscent of classical absolute stability criteria, which are sufficient for a range of incremental stability properties and input-to-state stability (ISS). Consequences of our results include sufficient conditions for the converging-input converging-state (CICS) property, and convergence to periodic solutions under periodic forcing.
Highlights
In systems and control theory, feedback interconnections comprising a linear system in the forward path and a static nonlinearity in the feedback path, as shown in Figure 1.1, are commonly referred to as Lur’e systems
Our focus is centred around incremental stability notions, input-to-state stability (ISS) and converging-input convergingstate (CICS) properties
A recent line of enquiry [2, 3, 4, 19, 20, 42, 43, 44] has been investigating to what extent classical absolute stability criteria can be modified to ensure ISS and state convergence properties of forced Lur’e systems
Summary
In systems and control theory, feedback interconnections comprising a linear system in the forward path and a static nonlinearity in the feedback path, as shown in Figure 1.1, are commonly referred to as Lur’e systems. We investigate certain stability and convergence properties of forced, infinite-dimensional, discrete-time Lur’e systems. A recent line of enquiry [2, 3, 4, 19, 20, 42, 43, 44] has been investigating to what extent classical absolute stability criteria can be modified to ensure ISS and state convergence properties of forced Lur’e systems. ISS properties underpin the paper [4], which considers the converginginput converging-state (CICS) property for finite-dimensional, continuous-time Lur’e systems. We consider incremental ISS notions for forced infinite-dimensional discrete-time Lur’e systems. For ve ∈ V , we will abuse notation and interchangeably write ve to denote an element of V and the constant function Z+ → V with value ve
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
