# Fault Tolerant Control for Switched Linear Systems by Dongsheng Du, Bin Jiang, Peng Shi

By Dongsheng Du, Bin Jiang, Peng Shi

This ebook provides updated learn and novel methodologies on fault prognosis and fault tolerant keep watch over for switched linear platforms. It offers a unified but neat framework of filtering, fault detection, fault analysis and fault tolerant keep watch over of switched platforms. it could actually as a result function an invaluable textbook for senior and/or graduate scholars who're attracted to understanding the cutting-edge of filtering, fault detection, fault prognosis and fault tolerant keep an eye on parts, in addition to contemporary advances in switched linear platforms.

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**Extra info for Fault Tolerant Control for Switched Linear Systems**

**Example text**

For examples, in [45] and [46], an H∞ filter formulation of robust FDI has been considered for uncertain LTI systems and Markovian jump linear systems. The issue of H∞ FD filter design for linear discrete-time systems with time delays is investigated in [41, 47]. c Springer International Publishing Switzerland 2015 D. Du, B. Jiang, and P. 1007/978-3-319-15162-5_2 17 18 2 Fault Detection for Discrete-Time Switched Systems On another research direction, switched systems have attracted increasing attention in the literature of control problems due to their great significance in theory and practical applications.

16) ¯ − ∑ δi (t)Fi x(t) ∑ δi (t)(Fi LC˜ + A¯ i)x(t) If the following conditions are fulfilled ¯ K = E¯ + KLC, Fi = Fi LC˜ + A¯ i , Fi L = −D¯ f . 17) is Fi = Ai 0 , −C −I L= 0 , I K= I + QC Q . 18) where matrices P and Q are free parameters to be determined. In order to guarantee the matrix K is non-singular, we assume that the matrix R is non-singular. 17), one can obtain the estimation error: N Ke(t + 1) = ∑ δi (t)Fi e(t). 20) i=1 where Si = K −1 Fi with K −1 = Si = I −QR−1 , −1 −C R + CQR−1 Ai + QR−1C QR−1 .

This means that FDI systems have to be robust to control inputs and unknown inputs, and at the same time enhance the sensitivity to the faults. Therefore, it is of great significance to design a model-based FD system. In reviewing the development of the theories and techniques for different FDI system designs, a number of results have been obtained in designing FDI system. For examples, in [46], an H∞ filter formulation of robust FDI has been considered for uncertain LTI systems. The issue of H∞ FD filter design for linear discrete-time systems with multiple time delays is investigated in [61].