Dr Bjorn Ruffer

A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exist points whose image under the monotone map is strictly smaller than the original point, in the component-wise partial ordering. Here it is shown how such points can be found numerically, leading to a recipe to compute order intervals that are contained in the region of attraction and where the monotone map acts essentially as a contraction. An important application is the numerical verification of so-called generalized small-gain conditions that appear in the stability theory of large-scale systems. © 2011 Springer Science+Business Media, LLC.

© 2014 IEEE.This paper addresses input-to-state stability (ISS) analysis for discrete-time systems using the notion of finite-step ISS Lyapunov functions. Here, finite-step Lyapunov functions are energy functions that decay after a fixed but finite number of steps, rather than at every time step. We establish non-conservative dissipativity and small-gain conditions for ISS of networks of discrete-time systems, by generalizing results in [1] and [2] to the case of ISS. The effectiveness of the results is illustrated through two examples.

© 2014 IEEE.For interconnected systems and systems of large size, aggregating information of subsystems studied individually is useful for addressing the overall stability. In the Lyapunov-based analysis, summation and maximization of separately constructed functions are two typical approaches in such a philosophy. This paper focuses on monotone systems which are common in control applications and elucidates some fundamental limitations of max-separable Lyapunov functions in estimating domains of attractions. This paper presents several methods of constructing sum- and max-separable Lyapunov functions for second order monotone systems, and some comparative discussions are given through illustrative examples.

This article is concerned with global asymptotic stability (GAS) of dynamical networks. The case when subsystems are integral input-to-state stable (iISS) has been recognized as notoriously difficult to deal with in the literature. In fact, the lack of energy dissipation for large input denies direct application of the small-gain argument for input-to-state stable (ISS) subsystems. Here for networks consisting of iISS subsystems it is demonstrated that a two-phase approach allows us to make use of the ISS small-gain argument by separating a trajectory into a transient and a subsequent ISS-like phase. In contrast to the previous iISS results, the two-phase approach immediately leads to a sufficiency criterion for GAS of general nonlinear networks, which is given in a matrix-like form (order condition). © 2013 AACC American Automatic Control Council.