Conditions of local identifiability of nonlinear systems under discrete observations (Q1333662)

The conditions for the parameter identification of systems of differential equations via discrete observations are discussed. For the system \[ \dot x= f(t, x, p),\qquad x(t_ 0)= x_ 0,\tag{1} \] where \(x\in \mathbb{R}\), parameter \(p= p^ i\in \Omega\subset \mathbb{R}\), \(i= 0,1,\dots, N- 1\), is piecewise-constant, the authors define at first \((k,m)\)-matrices \(w_ i(p_ 0)\) and a function \(F(p)\) and then they prove that if \(p_ 0\in D= \Omega^ m\) is a local minimum point of function \(F(p)\) and rank \(w_ i(p_ 0)= m\), \(i= 1,2,\dots, N\), then system (1) has a local identification at \(p_ 0\).