Positive 1D and 2D Systems

by Tadeusz Kaczorek

Overview

In the last decade a dynamic development in positive systems has been observed. Roughly speaking, positive systems are systems whose inputs, state variables and outputs take only nonnegative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear system behaviour can be found in engineering, management science, economics, social sciences, biology and medicine, etc. The basic mathematical tools for analysis and synthesis of linear systems are linear spaces and the theory of linear operators. Positive linear systems are defined on cones and not on linear spaces. This is why the theory of positive systems is more complicated and less advanced. The theory of positive systems has some elements in common with theories of linear and non-linear systems. Schematically the relationship between the theories of linear, non-linear and positive systems is shown in the following figure Figure 1.

Product Details

ISBN-13:	9781852335083
Publisher:	Springer-Verlag New York, LLC
Publication date:	10/28/2001
Series:	Communications and Control Engineering Series
Pages:	444
Product dimensions:	65.00(w) x 92.50(h) x 1.50(d)

Table of Contents

Elements of Probability Theory Uncertain Linear Systems and Robustness Linear Robust Control Design Some Limits of the Robustness Paradigm Probabilistic Methods for Robustness Monte Carlo Methods Randomized Algorithms in Systems and Control Probability Inequalities Statistical Learning Theory and Control Design Sequential Algorithms for Probabilistic Robust Design Sequential Algorithms for LPV Systems Scenario Approach for Probabilistic Robust Design Random Number and Variate Generation Statistical Theory of Radial Random Vectors Vector Randomization Methods Statistical Theory of Radial Random Matrices Matrix Randomization Methods Applications of Randomized Algorithms