# Reconfigurable Control of Nonlinear Dynamical Systems: A by Jan H. Richter

By Jan H. Richter

This learn monograph summarises strategies to reconfigurable fault-tolerant keep an eye on difficulties for nonlinear dynamical platforms which are in accordance with the fault-hiding precept. It emphasises yet isn't really restricted to accomplish actuator and sensor disasters. within the first half, the monograph begins with a huge advent of the keep watch over reconfiguration difficulties and goals in addition to summaries and causes of suggestions for linear dynamical structures. the answer is usually a reconfiguration block, which is composed of linear digital actuators in relation to actuator faults and linear digital sensors when it comes to sensor faults. the most benefit of the fault-hiding notion is the reusability of the nominal controller, which is still within the loop as an energetic process whereas the digital actuator and sensor adapt the keep an eye on enter and the measured output to the fault situation. the second one and 3rd components expand digital actuators and digital sensors in the direction of the periods of Hammerstein-Wiener platforms and piecewise affine structures. the most analyses situation balance restoration, setpoint monitoring restoration, and function restoration as reconfiguration goals. The fourth half concludes the monograph with descriptions of functional implementations and case reports. The ebook is basically meant for lively researchers and training engineers within the box of fault-tolerant regulate. because of many operating examples it's also appropriate for graduate students.

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**Sample text**

In particular, the fault-hiding approach is not available for nonlinear systems. This monograph addresses the extension of the fault-hiding principle to two classes of nonlinear systems, namely to HammersteinWiener systems and piecewise aﬃne systems. Chapter 2 Preliminaries Abstract. This chapter defines the notation for this monograph and recalls central notions from the literature that constitute the theoretical foundation of this monograph. These notions are linear matrix inequalities, polyhedra and polytopes, and classical as well as recent results from stability theory.

Inertia: Let ν− ( A), ν0 ( A), and ν+ ( A) denote the numbers (counting multiplicity) of eigenvalues of a symmetric matrix A with negative, zero, and positive real part, respectively. The triple In(A) (ν− ( A), ν0 ( A), ν+ ( A))T is called the inertia of A. The following lemma identifies congruence transformations as inertia-preserving operations. 1 (Congruence transformation [29]). If A is Hermitian and T is nonsingular, then the matrices A and T ∗ AT have the same inertia: In( A) = In(T ∗ AT).

C B C A pair of matrices (A, B), where A ∈ Rn×n , B ∈ Rn×m , is called stabilisable, if there exists a matrix K ∈ Rm×n such that A − BK is Hurwitz. A pair of matrices (C, A), where A ∈ Rn×n , C ∈ Rq×n , is called detectable, if there exists a matrix L ∈ Rn×q such that A − LC is Hurwitz. The following comparison functions are used [104]. A function F : S → R defined on a set S ⊂ Rn containing zero is positive definite if F(x) > 0 holds for all x ∈ S , x 0, and F(0) = 0. A class K function is a function α : R+ → R+ which is continuous, strictly increasing, and satisfies α(0) = 0.