Time-relevant stability of 2D systems

For many 2D systems, one of the independent variables plays a distinct role in the evolution of the trajectories; since often this special independent variable is time, we call such systems ‘time-relevant’. In this paper, we introduce a stability notion for time-relevant systems described by higher-order difference equations. We give algebraic tests in terms of the location of the zeros of the determinant of a polynomial matrix describing the system. We also give an LMI characterization of time-relevant stability involving only constant matrices.     

Stabilization of linear systems over networks with bounded packet loss and its use in model predictive control

This paper considers stabilization of discrete-time linear systems, where network exists for transmitting the sensor and controller information, and arbitrary bounded packet loss occurs in the sensor–controller link and the controller–actuator link. The stabilization of this system is transformed into the robust stabilization of a set of systems. The stability result for this system is specially applied on model predictive control (MPC) that explicitly considers the satisfaction of input and state constraints. Two synthesis approaches of MPC are presented, one parameterizing the infinite horizon control moves into a single state feedback law, the other into a free control move followed by the single state feedback law. Two simulation examples are given to illustrate the effectiveness of the proposed techniques.     

Note on stability of linear systems with time-varying delay

This note considers the stability of linear systems with a time-varying delay. We are interested in a simple Lyapunov–Krasovskii functional (LKF) approach without delay decomposition. In this category, all recent tractable results had a fixed bound on the allowable maximum size of the delay for years. We propose a new simple LKF including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function, and present a new result expressed in the form of LMIs. We show, by two well-known examples, that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time-delay.     

A second-order maximum principle for discrete-time bilinear control systems with applications to discrete-time linear switched systems

A powerful approach for analyzing the stability of continuous-time switched systems is based on using optimal control theory to characterize the “most unstable” switching law. This reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific “most unstable” switching law. For discrete-time switched systems, the variational approach received considerably less attention. This approach is based on using a first-order necessary optimality condition in the form of a maximum principle (MP), and typically this is not enough to completely characterize the “most unstable” switching law. In this paper, we provide a simple and self-contained derivation of a second-order necessary optimality condition for discrete-time bilinear control systems. This provides new information that cannot be derived using the first-order MP. We demonstrate several applications of this second-order MP to the stability analysis of discrete-time linear switched systems.     

Robust skeletonization using the discrete λ-medial axis

Medial axes and skeletons are notoriously sensitive to contour irregularities. This lack of stability is a serious problem for applications in e.g. shape analysis and recognition. In 2005, Chazal and Lieutier introduced the λ-medial axis as a new concept for computing the medial axis of a shape subject to single parameter filtering. The λ-medial axis is stable under small shape perturbations, as proved by these authors. In this article, a discrete λ-medial axis (DLMA) is introduced and compared with the recently introduced integer medial axis (GIMA). We show that DLMA provides measurably better results than GIMA, with regard to stability and sensibility to rotations. We give efficient algorithms to compute the DLMA, and we also introduce a variant of the DLMA which may be computed in linear-time.     

Stability analysis of networked control systems subject to packet-dropouts and finite-level quantization

This paper is concerned with the stability analysis of a networked control system, wherein communication from the controller to the plant input is through a digital channel subject to packet-dropouts and finite-level quantization. No acknowledgments of receipt are available to the controller. To alleviate the effect of packet-dropouts, the controller transmits tentative plant input sequences. Within this setup, we derive a sufficient condition for small ?^∞ signal ?^∞ stability of the networked control system. This condition requires the maximum number of consecutive packet-dropouts to be bounded. We also elucidate the trade-off which exists between the disturbance attenuation and the step size of the quantizer and the maximum number of consecutive packet-dropouts.     

Extra back-off flow control in multi-hop wireless networks

CSMA is the predominant distributed access protocol for wireless mesh networks. Originally designed for single-hop settings, CSMA can exhibit severe performance problems in multi-hop networks in terms of stability and end-to-end throughput. To ensure a smoother flow of packets, we examine an enhancement referred to as Extra Back-off (EB) flow control. In this enhanced scheme a node remains silent for a certain extra back-off time (imposed on top of the usual back-off time that is part of CSMA) after it has transmitted a packet, to give both the downstream and upstream neighbors the opportunity to transmit. EB flow control entails only a small modification to CSMA, preserving its distributed character. In order to examine the performance of EB flow control, we analyze a novel class of Markov models at the interface between classical tandem queues and interacting particle systems. The results demonstrate that EB flow control provides an effective mechanism for improving the end-to-end throughput performance.     

Stability radius of implicit dynamic equations with constant coefficients on time scales

This paper deals with the stability radii of implicit dynamic equations on time scales when the structured perturbations act on both the coefficient of derivative and the right-hand side. Formulas of the stability radii are derived as a unification and generalization of some previous results. A special case where the real stability radius and the complex stability radius are equal is studied. Examples are derived to illustrate results.     

Optimality and stability of the K-hyperline clustering algorithm

K-hyperline clustering is an iterative algorithm based on singular value decomposition and it has been successfully used in sparse component analysis. In this paper, we prove that the algorithm converges to a locally optimal solution for a given set of training data, based on Lloyd’s optimality conditions. Furthermore, the local optimality is shown by developing an Expectation-Maximization procedure for learning dictionaries to be used in sparse representations and by deriving the clustering algorithm as its special case. The cluster centroids obtained from the algorithm are proved to tessellate the space into convex Voronoi regions. The stability of clustering is shown by posing the problem as an empirical risk minimization procedure over a function class. It is proved that, under certain conditions, the cluster centroids learned from two sets of i.i.d. training samples drawn from the same probability space become arbitrarily close to each other, as the number of training samples increase asymptotically.     

An explicit predictor-corrector solver with application to seismic wave modelling

Wave-equation-based forward modelling using explicit finite-difference methods is a standard technique for calculating synthetic seismograms. The stability criterion restricts the size of the time step. In this paper a predictor–corrector method for solving the wave equation is described which allows the use of a larger time step. A stability analysis of the method is also carried out. Parallel implementation of the algorithm is described for a distributed computing environment which makes use of MPI and PVM message passing calls for communication between processors.