A Generalized Framework of Linear Multivariable Control

A Generalized Framework of Linear Multivariable Control proposes a number of generalized models by using the generalized inverse of matrix, while the usual linear multivariable control theory relies on some regular models.

The book supports that in H-infinity control, the linear fractional transformation formulation is relying on the inverse of the block matrix. If the block matrix is not regular, the H-infinity control does not apply any more in the normal framework. Therefore, it is very important to relax those restrictions to generalize the classical notions and models to include some non-regular cases.

This book is ideal for scholars, academics, professional engineer and students who are interested in control system theory.

Presents a comprehensive set of numerical procedures, algorithms, and examples on how to deal with irregular modelsProvides a summary on generalized framework of linear multivariable control that focuses on generalizations of models and notionsIntroduces a number of generalized models by using the generalized inverse of matrix

1. Introduction 2. Mathematical preliminaries 3. Generalized inverse of matrix and solution of linear system equation 4. Polynomial fraction description 5. Stability 6. Fundamental approaches to control system analysis 7. Determination of finite and infinite frequency structure of a rational matrix 8. The solution of a regular PMD and the set of impulsive free initial conditions 9. A refined resolvent decomposition of a regular polynomial matrix and application to the solution of regular PMDs 10. Frequency structures of generalized companion form and application to the solution of regular PMDs 11. A generalized chain-scattering representation and its algebraic system properties 12. Realization of behavior 13. Related extensions to system well-posedness and internal stability 14. Nonstandard H_∞ control problem: A generalized chain-scattering representation approach 15. Internet congestion control: A linear multivariable control look 16. Conclusions and further research