Ebook: Positive 1D and 2D Systems

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.

---

The presence of uncertainty in a system description has always been a critical issue in control. Moving on from earlier stochastic and robust control paradigms, the main objective of this book is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. Using so-called randomized algorithms, this emerging area of research guarantees a reduction in the computational complexity of classical robust control algorithms and in the conservativeness of methods like H? control. Features: · self-contained treatment explaining the genesis of randomized algorithms in the principles of probability theory to their use for robust analysis and controller synthesis; · comprehensive treatment of sample generation, including consideration of the difficulties involved in obtaining identically and independently distributed samples; · applications of randomized algorithms in congestion control of high-speed communications networks and the stability of quantized sampled-data systems. Randomized Algorithms for Analysis and Control of Uncertain Systems will be of certain interest to control theorists concerned with robust and optimal control techniques and to all control engineers dealing with system uncertainties.

---

The presence of uncertainty in a system description has always been a critical issue in control. Moving on from earlier stochastic and robust control paradigms, the main objective of this book is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. Using so-called randomized algorithms, this emerging area of research guarantees a reduction in the computational complexity of classical robust control algorithms and in the conservativeness of methods like H? control. Features: · self-contained treatment explaining the genesis of randomized algorithms in the principles of probability theory to their use for robust analysis and controller synthesis; · comprehensive treatment of sample generation, including consideration of the difficulties involved in obtaining identically and independently distributed samples; · applications of randomized algorithms in congestion control of high-speed communications networks and the stability of quantized sampled-data systems. Randomized Algorithms for Analysis and Control of Uncertain Systems will be of certain interest to control theorists concerned with robust and optimal control techniques and to all control engineers dealing with system uncertainties.
Content:
Front Matter....Pages I-XIII
Positive matrices and graphs....Pages 1-49
Continuous-time and discrete-time positive systems....Pages 51-126
Reachability, controllability and observability of positive systems....Pages 127-172
Realisation problem of positive 1D systems....Pages 173-240
2D models of positive linear systems....Pages 241-273
Controllability and minimum energy control of positive 2D systems....Pages 275-309
Realisation problem for positive 2D systems....Pages 311-366
Back Matter....Pages 367-431

---

The presence of uncertainty in a system description has always been a critical issue in control. Moving on from earlier stochastic and robust control paradigms, the main objective of this book is to introduce the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. Using so-called randomized algorithms, this emerging area of research guarantees a reduction in the computational complexity of classical robust control algorithms and in the conservativeness of methods like H? control. Features: · self-contained treatment explaining the genesis of randomized algorithms in the principles of probability theory to their use for robust analysis and controller synthesis; · comprehensive treatment of sample generation, including consideration of the difficulties involved in obtaining identically and independently distributed samples; · applications of randomized algorithms in congestion control of high-speed communications networks and the stability of quantized sampled-data systems. Randomized Algorithms for Analysis and Control of Uncertain Systems will be of certain interest to control theorists concerned with robust and optimal control techniques and to all control engineers dealing with system uncertainties.
Content:
Front Matter....Pages I-XIII
Positive matrices and graphs....Pages 1-49
Continuous-time and discrete-time positive systems....Pages 51-126
Reachability, controllability and observability of positive systems....Pages 127-172
Realisation problem of positive 1D systems....Pages 173-240
2D models of positive linear systems....Pages 241-273
Controllability and minimum energy control of positive 2D systems....Pages 275-309
Realisation problem for positive 2D systems....Pages 311-366
Back Matter....Pages 367-431
....