By Katalin M. Hangos, Jozsef Bokor, Gabor Szederkenyi

This easy textual content makes the advanced yet robust equipment of non-linear keep an eye on obtainable to strategy engineers. not just does it hide the required arithmetic, however it regularly refers back to the widely-known finite-dimensional linear time-invariant non-stop case as a foundation for extension to the nonlinear situation.

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15) 2. 16) 3. 1 Signals 15 4. 18) 5. 19) λt where λ ∈ C and eλ (t) = e . 5 Lq Signal Spaces and Signal Norms Signals with similar mathematical properties belong to signal spaces which are usually equipped by suitable signal norms. Lq spaces are the most frequently used general signal spaces described below. 6 (Lq spaces, scalar case) For q = 1, 2, . . e. 1 in the Appendix for the defining properties of norms). 7 (q-norm, scalar case) Let f ∈ Lq [0, ∞) for q = 1, 2, . . 21) It is known that Lq [0, ∞) are complete normed linear spaces (Banach spaces) with respect to the q-norms.

2. 13) The most important properties (among others) of Laplace transformation that we will use later are the following: Let f, g ∈ Λ. Then the following equalities hold 1. 15) 2. 16) 3. 1 Signals 15 4. 18) 5. 19) λt where λ ∈ C and eλ (t) = e . 5 Lq Signal Spaces and Signal Norms Signals with similar mathematical properties belong to signal spaces which are usually equipped by suitable signal norms. Lq spaces are the most frequently used general signal spaces described below. 6 (Lq spaces, scalar case) For q = 1, 2, .

They will be used in the rest of the book. The linear time-invariant (LTI) state-space model is introduced first, since it serves as a basic case for all extensions towards the nonlinear state-space representation forms. The linear time-varying parameter (LTV) and linear parameter-varying (LPV) systems are seen as intermediate cases between the basic reference LTI and the general nonlinear cases. The general and input-affine state-space models, introduced last, are the basis of all the nonlinear analysis and control techniques described in this book, are also introduced here.