## Full-order perfect observers for continuous-time linear systems.(English)Zbl 1007.93008

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 $$CB\neq 0$$.

### MSC:

 93B07 Observability

### Keywords:

perfect observers; linear systems