Titlebook: Control Theory for Linear Systems; Harry L. Trentelman,Anton A. Stoorvogel,Malo Hautu Book 2001 Springer-Verlag London 2001 Geometric Cont

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Introduction,tions. The ultimate product of a control system design problem is a physical device that, if connected to the to be controlled physical system, makes it behave according to the specifications. This device is called a controller.

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Systems with inputs and outputs,Here . and . are maps between suitable spaces (or matrices of suitable dimensions) and the functions . and .are usually considered to be defined on the real axis ? or on any subinterval of it. In particular, one often assumes the domain of definition to be the nonnegative part of ?. The function . i

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Controlled invariant subspaces,space and stabilizability subspace. The notion of controlled invariance is of fundamental importance in many of the feedback design problems that the reader will encounter in this book. We will apply these concepts to a number of basic feedback design problems, among which the problem of disturbance

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Conditioned invariant Subspaces,onnected with maintaining and recovering information on the state vector of an observed linear system. It is shown that conditioned invariance and controlled invariance are, in fact, dual concepts. This fact makes it possible to ‘translate’ many of the results obtained in the previous chapter on con

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System zeros and the weakly unobservable subspace,system ∑ given by the equations.. = . + .,..and introduce an important polynomial matrix associated with this system, the system matrix of ∑. Using the system matrix, we introduce the concepts of transmission polynomials, and zeros of the system ∑. Next, we discuss the weakly unobservable subspace,

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System invertibility and the strongly reachable subspace,te in case the input is a distribution. We will do this using the distributional set-up discussed in the Appendix on distributions. We will derive the exact formulas for the state trajectory and output corresponding to a given initial state and impulsive-smooth distributional input.

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,, control and robustness,bust stability. We would like to guarantee the stability of a plant even if the model on the basis of which the controller was designed is not a perfect representation of the behavior of the plant. On the other hand it also yields a clear link between several classical frequency-domain methods and m

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