Geometric control of patterned linear systems (Q409645)

The book deals with a new class of linear systems, called patterned linear systems, characterized by the property that they sustain or carry a pattern which is mathematically induced by system matrices that share a common base transformation. Meaningful physical examples are circulant systems; systems structured as chains, triangular Toeplitz systems arising in the discretization of PDE models and systems structured as trees, such as hierarchical systems. The geometric approach based on the notion of invariant subspaces is used to characterize basic properties of patterned systems such as patterned controllability, patterned observability and patterned Kalman decompositions. The synthesis of the controller solving some classical problem such as output stabilization, disturbance decoupling, stabilization by measurement feedback, and the regulator problem is provided in geometric terms. The book is intended for researchers in system control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems and it is self-contained, but a first year graduate course in linear control systems is desirable as well as the knowledge of fundamental notions of the geometric approach. Anyway, a number of examples, of higher dimension than one may typically see in a text, are provided that illustrate the geometric and abstract algebra concepts used in linear geometric control. The book is organized as follows. Chapter 1 gives an introduction to the subject of patterned linear systems. Chapter 2 gives the essential linear algebra background for linear geometric control theory. In the following three chapters, Part I, the geometric theory of patterned linear systems is described. Chapter 3 introduces the machinery to build up patterned linear systems, particularly patterned maps and their geometric and abstract algebra properties. Chapter 4 introduces patterned linear systems and presents their system theoretic properties such as controllability, observability, and decompositions. Chapter 5 studies several of the main control synthesis problems of linear multivariable control. In the last four chapters, Part II, specific patterns and their applications are considered. Chapter 6 is devoted to ring systems, Chapter 7 to chain patterns and in Chapter 8 trees are briefly described. Chapters 9 is devoted to future research directions. Chapter 10 contains the conclusions.