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 investigates the controller design problem for a class of nonlinear systems by introducing a Takagi-Sugeno system with nonlinear consequent parts. In this regard, it is assumed that the measured variables are available at discrete-time instants with non-periodic sampling time. Using the Lyapunov-Krasovskii stability theory, some conditions are presented and expressed in the form of linear matrix inequalities such that the closed-loop system is asymptotically stable and achieves a prescribed H~ performance level. Finally, a numerical examples is provided to illustrate the effectiveness of the proposed method.

Controller Design for Takagi-Sugeno Fuzzy Systems with Nonlinear Consequent Part Via Sampled-Data Measurements

This chapter is concerned with a delayed non-fragile H∞ control scheme for an offshore steel jacket platform subject to self-excited nonlinear hydrodynamic force and external disturbance. By intentionally introducing a time-delay into the control channel, a delayed robust non-fragile H∞ controller is designed to reduce the vibration amplitudes of the offshore platform. The positive effects of time-delays on the non-fragile H∞ control for the offshore platform are investigated. It is shown through simulation results that (i) the proposed delayed non-fragile H∞ controller is effective to attenuate vibration of the offshore platform, (ii) the control force required by the delayed non-fragile H∞ controller is smaller than the one by the delay-free non-fragile H∞ controller, and (iii) the time-delays can be used to improve the control performance of the offshore platform.

Xian-Ming Zhang

Papers

Controller Design for Takagi-Sugeno Fuzzy Systems with Nonlinear Consequent Part Via Sampled-Data Measurements

Delayed Robust Non-fragile H∞ Control