By Hao Yang
From the reviews:
“Fault detection and fault tolerant regulate innovations have acquired broad cognizance within the box of continuous-time, particularly linear, platforms. … as a result the monograph in query is a really compatible addition to this box. … there's a record of references, with 157 entries, that is an exceptional compendium of the literature within the box. ordinarily, this monograph is an effective addition to the industry-relevant study within the box of fault detection and fault tolerant control.” (Amit Patra, Mathematical studies, factor 2011 e)
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Additional resources for Fault Tolerant Control Design for Hybrid Systems
Sample text
30) hold at a given t(k+1) j . 35). 2 can be applied to guarantee the asymptotic stability of the origin of the HS. 2 Overall Fault Tolerant Regulation This section extends the classical output regulation theories to hybrid nonlinear systems and analyzes its fault tolerance in the presence of continuous faults modeled by the exosignals. 39) with measurable state x ∈ ℜn , input u ∈ ℜ p , output y ∈ ℜm . The regulated error e denotes the output tracking error between y and the continuous reference signal yr (x) : ℜn → ℜm .
This completes the proof. 67) without ui and fˆic . exi denotes the state estimation error using observer i. 98) are invoked to estimate the current mode simultaneously in Δ t j . Set the initial states of observers to x(t ˆ − j ) at t = t j . , for mode i without input, |exi | converges faster than |ex j |, ∀ j ∈ Q, j = i . This is a quite general condition for switching control problem as for instance in [20],[129] and [68]. Roughly speaking, it means that all the modes are not overlapping. The identifiability is analyzed in the following lemma.
Global passivity implies the stability as shown below. 7. 112) is globally passive, then the origin of the system is stable in spite of faults. 113), we can choose ε2i > 0 such that Vi < ε2i leads to (α1i )−1 (Vi ) < ε . Pick ε3 = mini [ε2i ], since Etr tends to zero as x(0) goes to the origin, we can choose ε4 such that |x(0)| < ε4 results in maxi [α2i (|x(0)|) + Etr (x(0))] < ε3 . 4 Global Passivity 45 mode 1 mode 2 mode 3 mode 4 mode 5 mode 6 healthy faulty healthy faulty healthy healthy ...