There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Time-delay systems: an overview of some recent advances and open problems

Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...

/pdf/higher-order-sliding-modes-differentiation-and-output-438zdzb0ld.pdf

Higher-order sliding modes, differentiation and output-feedback control

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

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

Vision Based Tracking for a Mini-Rotorcraft Using Vanishing Points

A model is developed for the investigation of an enzymatic diffusion-reaction system. The aim is to analyze the dynamic behavior of three different species, the modification of their enzymatic kinetic properties and the existence of complex behaviors resulting of the catalytic activity induced by immobilization of acetylcholinesterase into artificial membrane enzymatically inactive. We report results that make possible the characterization and prediction of complex behaviors as well as a qualitative/quantitative analysis of the system stability via bifurcation diagram which allows to study: i) the effect of the initial substrate concentration in the reservoir and ii) the effect of reaction-permeation modulus of the membrane as bifurcation parameters.

Modelling of acetylcholinesterase immobilized into artificial membrane.

In the study and control of general dynamical systems the energy stored in the system is an important information. Some autonomous dynamical systems (i.e. with input equal to zero) have the important property that the amount of energy stored in the system remains unchanged or even decreases. This gives rise to the definition of Dissipative systems which is very useful in the synthesis of control systems. Different definitions are introduced to distinguish different classes of systems. Linear systems and nonlinear systems are two important classes of dynamical systems which for simplicity reasons have been usually studied separately in what concerns their dissipative properties. Linear systems whose stored energy remains constant or decreases are called Positive Real (PR) systems or Strictly Positive Real (SPR) respectively while we usually reserve the term dissipative for nonlinear systems in general. We can certainly use the term dissipative for a linear system however the term positive real is only reserved for transfer functions. Furthermore, there exists several important subclasses of linear and nonlinear systems with slightly different properties which are important in the analysis. This will lead us to introduce a series of different definitions of PR and dissipative systems. This chapter deals with Positive Real systems. The next chapter will be devoted to dissipative nonlinear systems.

Positive Real Systems

In this paper a modi"ed version of the standard least-squares algorithm is presented. The aim is to use the proposed modi"ed LS algorithm in linear time-varying systems. The proposed modi"cation involves the addition of extra terms to both the parameter estimates’ and the covariance’s update laws. We establish a series of properties on the identi"cation error, the parameter estimates and the covariance matrix. These properties are important in an adaptive control context, because LS algorithms provide an easy way of modifying the parameter estimates in order to avoid singular points in the control scheme. ( 2000 Elsevier Science Ltd. All rights reserved.

Rogelio Lozano

Papers

Vision Based Tracking for a Mini-Rotorcraft Using Vanishing Points

Modelling of acetylcholinesterase immobilized into artificial membrane.

Positive Real Systems

Brief Paper Identi"cation of linear time-varying systems using a modi"ed least-squares algorithm q

Synchronized flight formation of quadrotors