Exact observer‐based structures for arbitrary compensators

Enhanced distinguishability in Supervisory Fault Tolerant Control

“…Proof: Based on the observer-based structures (Alazard & Apkarian, 1999), the detection filters defined by (4) can be rewritten without loss of generality according to ( )…”

“…are the states of (4) reformulated by means of observer-based structures (Alazard & Apkarian, 1999) for the case of augmented-order filters, i.e. n n i F > .…”

“…In the interest of brevity, the mechanization equations leading to this reformulation are omitted here. The interested reader can refer to (Alazard & Apkarian, 1999), (Cieslak et al, 2010) for some guidelines on this reformulation.…”

Robust observer–controller compensator design using the loop shaping design procedure and the algebraic method

“…Nevertheless, this shows that the observer design of VS can be derived from the LCF of the central controller. Moreover, the term H −1 Y l in Equation (7) corresponds to Q in Equation (8). This means that K v (s) is a subset of the YKP since H is a unit over RH ∞ .…”

“…However, VS is simpler than the YKP structure. Noted that VS in Figure 1(a) is stable itself while K v (s) of Equation (7) and K YK (s) of Equation (8) are not necessarily stable.…”