Observability of quasimonotonic systems (Q1108238)

Consider the plant \(\dot x=F(x)\), \(x\in R^ m\), \(y=H(x)\), \(y\in R^ p\), where F, H are continuously differentiable with \(F(0)=0\), \(H(0)=0\), and F is quasimonotonic (i.e. \(\partial F_ i/\partial x_ j\geq 0\), \(i\neq j)\). The paper deals with the construction of an operator G: \({\mathcal L}\to R^ m\) (\({\mathcal L}\) denotes a vector space of functions of a scalar argument that take their values in \(R^ p)\) which in the case of an undistorted signal y(t) exactly reproduces x(t). In the case of bounded noise which distorts y(t) it yields minimum observation error, and in the case when y(t) belongs to the nonnegative (positive) cone of \({\mathcal L}\) it yields nonnegative (positive) solutions. When F is unknown the author proposes the following approach (dynamic observation): using a plant model \(\dot z=F_ 0(z,u)\), \(z\in R^ m\), \(u\in R^ p\), realized on a computer, one has to design the control u in order to achieve z(t)\(\to x(t)\) asymptotically. An illustrative example is finally given.