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 networked state feedback stabilization control problem for an offshore platform. By transforming the networked closed-loop system of the offshore platform into a nonlinear delay system with time-varying delays, a new networked state feedback controller is designed to improve the control performance of the offshore platform. Simulation results demonstrate that the developed networked control scheme is effective to attenuate the oscillation amplitudes of the offshore platform significantly. In addition, in the cases of different lower bounds of network-induced delay, the maximum admissible upper bounds of the delay in the networked offshore platform are investigated.

Active Control Design for Networked Offshore Platforms

This paper is concerned with the problem of the robust sampled-data H∞ control for an offshore steel jacket platform subject to the self-excited wave force and the external disturbance. First, by using the input delay method, the corresponding closed-loop system with the sampling measurements is transformed into a continuous-time system. Then, based on a Lyapunov functional, the H∞ performance is established and the stability criteria for the closed-loop system is derived. Finally, the effectiveness of the proposed robust sampled-data H∞ controller is demonstrated by a simulation example. The simulation results show that the designed controller is effective to control the offshore platform, Moreover, to obtain almost the same control performance, the required control force under the robust sampled-data H∞ controller is smaller than the one under the robust H∞ controller.

Robust sampled-data H∞ control for offshore steel jacket platforms

This paper is concerned with the stability of networked control systems in the discrete-time domain. A new bounding technique is proposed to estimate some finite-sum terms appearing in the forward difference of the chosen Lyapunov functional. This new bounding technique can provide tighter upper bounds for some finite-sum terms and avoid overly bounding for the finite-sum terms. Then a novel delay-dependent stability criterion is derived by using this new bounding technique. Compared with some existing stability criteria in the published literature, the novel stability criterion is proven theoretically to be less conservative and is shown to be of smaller numerical complexity.

A novel stability criterion for networked control systems using a new bounding technique

This chapter investigates the effect of a time-delay on dynamic output feedback control of an offshore steel jacket platform subject to a nonlinear wave-induced force. First, a conventional dynamic output feedback controller is designed to reduce the internal oscillations of the offshore platform. It is found that the designed controller is of a larger gain in the sense of Euclidean norm, which demands a larger control force. Second, a time-delay is introduced intentionally to design a new dynamic output feedback controller such that (i) the controller is of a small gain in the sense of Euclidean norm and (ii) the internal oscillations of the offshore platform can be dramatically reduced. It is shown through simulation results that purposefully introducing time-delays can be used to improve control performance.

Delayed Dynamic Output Feedback Control

This paper is concerned with extended dissipativity analysis of memristive neural networks with time-varying delays. Using the characteristic function technique, a tractable model of a memristive neural network is obtained. This model is similar to a neural network with polytopic uncertain synaptic weights, enabling us to construct a parameter-dependent Lyapunov functional. By combining this functional and some integral inequalities, a novel extended dissipativity criterion is obtained in terms of linear-matrix-inequalities, where different Lyapunov matrices are used for each form of the memristive neural network. Through a numerical example, this criterion is shown to be less conservative than the one based on a common Lyapunov functional.

Xian-Ming Zhang

Papers

Active Control Design for Networked Offshore Platforms

Robust sampled-data H∞ control for offshore steel jacket platforms

A novel stability criterion for networked control systems using a new bounding technique

Delayed Dynamic Output Feedback Control

Extended Dissipativity Analysis of Delayed Memristive Neural Networks Based on A Parameter-Dependent Lyapunov Functional