Full-order perfect observers for continuous-time linear systems (Q1596523)

A new concept of the full-order perfect observer for standard linear systems is presented. Conditions for the existence of the perfect observer are established, and its design procedure is derived. It is proved that: Theorem. There exists a full-order perfect observer of the form \[ E{d \overline x\over dt}=A\overline x+Bu+K(C\overline x-y) \] for the standard system \[ {dx\over dt}= Ax+Bu,\quad x(0)=x_0,\;y=C_x \] with the derivative output feedback \(u=v-F{dy\over dt}= v-FC{dx\over dt}\) were \(E={\mathbf I}_{\mathbf n}+BFC\) \[ x(t)\in \mathbb{R}^n,\;u(t)\in\mathbb{R}^m,y(t) \in\mathbb{R}^p, E,A\in\mathbb{R}^{n\times m},\;C\in\mathbb{R}^{p\times m}, F\in\mathbb{R}^{m\times p} \] if \(\text{rank} {I_ns- A\brack C}=n\) for all \(s\in\mathbb{C}\) and \(CB\neq 0\).