Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

http://www.ece.ualberta.ca/~tchen/papers/Gao_auto08n1.pdf

A new delay system approach to network-based control

Event-triggered consensus of multiagent systems (MASs) has attracted tremendous attention from both theoretical and practical perspectives due to the fact that it enables all agents eventually to reach an agreement upon a common quantity of interest while significantly alleviating utilization of communication and computation resources. This paper aims to provide an overview of recent advances in event-triggered consensus of MASs. First, a basic framework of multiagent event-triggered operational mechanisms is established. Second, representative results and methodologies reported in the literature are reviewed and some in-depth analysis is made on several event-triggered schemes, including event-based sampling schemes, model-based event-triggered schemes, sampled-data-based event-triggered schemes, and self-triggered sampling schemes. Third, two examples are outlined to show applicability of event-triggered consensus in power sharing of microgrids and formation control of multirobot systems, respectively. Finally, some challenging issues on event-triggered consensus are proposed for future research.

/pdf/an-overview-of-recent-advances-in-event-triggered-consensus-3rmvpx3qkr.pdf

An Overview of Recent Advances in Event-Triggered Consensus of Multiagent Systems

A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay

This paper is concerned with the problem of designing distributed event-triggered H∞ filters over sensor networks subject to heterogeneous coupling intercommunication delays. A new distributed event-triggered scheme is proposed to determine whether or not each sensor's current sampled data should be broadcasted and transmitted to its underlying neighboring nodes through the communication network. In this scheme, each sensor node is able to make its own decisions to broadcast and transmit only when its local measurement output error exceeds a designed threshold. Heterogeneous coupling delays are incorporated in the intercommunication between the specific sensor node and its interacting neighbors. A refined technique is proposed to realize the complicated decoupling among the exchanged measurement outputs in the presence of coupling intercommunication delays. Then the resulting filter error system is modeled by a new delay system subject to finite time-varying “state” delays. Based on the Lyapunov-Krasovskii functional method, a sufficient condition for distributed event-triggered H∞ filter design is established, from which the desired filter parameters and the triggering parameter in the event condition can be co-designed. The filter design problem is posed in terms of linear matrix inequalities. A quarter-car suspension model is finally presented to show the effectiveness and feasibility of the developed theoretical results.

Distributed event-triggered H ∞ filtering over sensor networks with coupling delays

This paper deals with the event-triggered distributed H ∞ filtering for a class of networked systems with sensor networks. The topology of the sensor network is supposed to be time-varying. Whether or not a sampled data packet of a sensor node should be transmitted to its neighbors is determined by a predefined event-triggering condition, which closely depends on the variation of the sensor network topology. By modelling the filtering error system as a switched linear system with time-varying delays, a bounded real lemma (BRL) is derived using Lyapunov-Krasovskii functional approach. Based on the BRL, a sufficient condition on the existence of desired H ∞ filters is obtained in terms of linear matrix inequalities. An algorithm to the design of both filter parameters and event-triggering parameters is given. It is shown through a numerical example that the proposed method can not only save significantly precious communication resources, and maintain some certain system performance as well.

Event-triggered distributed H ∞ filtering for networked systems with switching topologies

The last few decades have witnessed the rapid development of networked control systems due to their significant advantages and they have been applied to variant industrial areas such as unmanned surface vehicles, unmanned space vehicles, smart grids, wastewater treatment processes, Internet-based teleoperation, intelligent transportation systems and so on [...]

https://www.mdpi.com/2079-9292/8/5/552/pdf

Recent Developments in Time-Delay Systems and Their Applications

This paper is concerned with the problem of delay-dependent Hinfin control for linear discrete-time systems with time-varying delay. A new finite sum inequality is first established to derive a delay-dependent condition, under which the resulting closed-loop system is asymptotically stable (internally stable) with a prescribed Hinfin attenuation level via a memoryless state feedback. Then, an iterative algorithm involving convex optimization is proposed to obtain a suboptimal Hinfin controller. Finally, a numerical example is given to show the effectiveness of the proposed method

A New Finite Sum Inequality for Delay-Dependent H&#8734; Control of Discrete-Time Delay Systems

This paper provides a brief overview of delayed feedback control schemes for offshore structures. Two simplified models of offshore steel jacket structures are listed first. Then based on the dynamic models of offshore structures, several active control strategies including delayed H ∞ control and delayed integral sliding mode control by using pure delayed signals and using current as well as delayed signals of the systems are outlined, respectively. Finally, some challenging problems and potential research directions about delayed feedback control for offshore structures are presented.

Xian-Ming Zhang

Papers

Distributed event-triggered H ∞ filtering over sensor networks with coupling delays

Event-triggered distributed H ∞ filtering for networked systems with switching topologies

Recent Developments in Time-Delay Systems and Their Applications

A New Finite Sum Inequality for Delay-Dependent H∞ Control of Discrete-Time Delay Systems

A brief overview of delayed feedback control for offshore structures

Xian-Ming Zhang

Papers

Distributed event-triggered H ∞ filtering over sensor networks with coupling delays

Event-triggered distributed H ∞ filtering for networked systems with switching topologies

Recent Developments in Time-Delay Systems and Their Applications

A New Finite Sum Inequality for Delay-Dependent H&#8734; Control of Discrete-Time Delay Systems

A brief overview of delayed feedback control for offshore structures

A New Finite Sum Inequality for Delay-Dependent H∞ Control of Discrete-Time Delay Systems