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

The gain-scheduling approach is perhaps one of the most popular non-linear control design approaches which has been widely and successfully applied in fields ranging from aerospace to process control. Despite the wide application of gainscheduling controllers and a diverse academic literature relating to gain-scheduling extending back nearly thirty years, there is a notable lack of a formal review of the literature. Moreover, whilst much of the classical gain-scheduling theory originates from the 1960s, there has recently been a considerable increase in interest in gain-scheduling in the literature with many new results obtained. An extended review of the gain-scheduling literature therefore seems both timely and appropriate. The scope of this paper includes the main theoretical results and design procedures relating to continuous gain-scheduling (in the sense of decomposition of non-linear design into linear sub-problems) control with the aim of providing both a critical overview and a useful entry point...

/pdf/survey-of-gain-scheduling-analysis-design-25aocvbxbn.pdf

Survey of Gain-Scheduling Analysis & Design

This paper is concerned with the design of gain-scheduled controllers for uncertain linear parameter-varying systems. Two alternative design techniques for constructing such controllers are discussed. Both techniques are amenable to linear matrix inequality problems via a gridding of the parameter space and a selection of basis functions. These problems are then readily solvable using available tools in convex semidefinite programming. When used together, these techniques provide complementary advantages of reduced computational burden and ease of controller implementation. The problem of synthesis for robust performance is then addressed by a new scaling approach for gain-scheduled control. The validity of the theoretical results are demonstrated through a two-link flexible manipulator design example. This is a challenging problem that requires scheduling of the controller in the manipulator geometry and robustness in face of uncertainty in the high-frequency range.

Advanced gain-scheduling techniques for uncertain systems

LPV control and full block multipliers

• Facts from convex analysis. LMI’s: history, algorithms and software. • The role of LMI’s in dissipativity Stability and nominal performance. Analysis results. • From analysis to synthesis. State-feedback, estimation and output-feedback synthesis. • From nominal to robust stability, robust performance and robust synthesis. • IQC’s and multipliers. Relations to classical tests and to μ-theory. • Mixed control problems and parameter-varying systems and control design.

http://www.eeci-institute.eu/pdf/M012/lec1.pdf

Linear Matrix Inequalities in Control

Regulatorer anvands i manga tillampningar for att forbattra prestanda ochegenskaper hos fordon och farkoster av olika slag, t ex flygplan och raketer.Beroende pa olika faktorer, som hastighet och h ...

/pdf/methods-for-robust-gain-scheduling-4czkjp3vwo.pdf

Methods for robust gain scheduling

Data driven local coordinates for multivariable linear systems and their application to system identification

The use of an over-parametrized state-space model for system identification has some clear advantages: A single model structure covers the entire class of multivariable systems up to a given order. The over-parametrization also leads to the possibility to choose a numerically stable parametrization. During the parametric optimization the gradient calculations constitute the main computational part of the algorithm. Consequently using more than the minimal number of parameters required slows down the algorithm. However, we show that for any chosen (over)-parametrization it is possible to reduce the gradient calculations to the minimal amount by constructing the parameter subspace which is orthonormal to the tangent space of the manifold representing equivalent models.

/pdf/system-identification-using-an-over-parametrized-model-class-1obliybdab.pdf

System identification using an over-parametrized model class-improving the optimization algorithm

http://www.diva-portal.org/smash/get/diva2:315982/FULLTEXT02

An IQC-Based Stability Criterion for Systems with Slowly Varying Parameters

https://www.diva-portal.org/smash/get/diva2:316286/FULLTEXT02

IQC Synthesis based on Inertia Constraints

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