9 research outputs found
Convex searches for discrete-time Zames-Falb multipliers
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 that any IIR multipliers can be phase-substituted by an
arbitrarily large order FIR multiplier. We show that searches in discrete-time
for FIR multipliers are effective even for large orders. As expected, the
numerical results provide the best -stability results in the
literature for slope-restricted nonlinearities. Finally, we demonstrate that
the discrete-time search can provide an effective method to find suitable
continuous-time multipliers.Comment: 12 page
Phase limitations of Zames-Falb multipliers
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 applicability is clarified; its relation to the Kalman conjecture is
illustrated with a classical example from the literature. It is demonstrated
that there exist fourth-order plants where the existence of a suitable
Zames-Falb multiplier can be discarded and for which simulations show unstable
behavior. A novel phase-limitation for discrete-time Zames-Falb multipliers is
developed. Its application is demonstrated with a second-order counterexample
to the Kalman conjecture. Finally, the discrete-time limitation is used to show
that there can be no direct counterpart of the off-axis circle criterion in the
discrete-time domain
From classical absolute stability tests towards a comprehensive robustness analysis
In this thesis, we are concerned with the stability and performance analysis of feedback interconnections comprising a linear (time-invariant) system and an uncertain component subject to external disturbances. Building on the framework of integral quadratic constraints (IQCs), we aim at verifying stability of the interconnection using only coarse information about the input-output behavior of the uncertainty
LMI searches for anticausal and noncausal rational Zames-Falb multipliers
AbstractGiven a linear time-invariant plant, the search for a suitable multiplier over the class of Zames–Falb multipliers is a challenging problem which has been studied for several decades. Recently, a new linear matrix inequality search has been proposed over rational and causal Zames–Falb multipliers. This letter analyzes the conservatism of the restriction to causality on the multipliers and presents a complementary search for rational and anticausal multipliers. The addition of a Popov multiplier to the anticausal Zames–Falb multiplier is implemented by analogy with the causal search. As a result, a search over a noncausal subset of Zames–Falb multipliers is obtained. A comparison between all the search methods proposed in the literature is given