A separation principle for affine systems (Q1874799)

For the nonlinear control system \[ \dot x=A(x)+B(x)u,\quad y= h(x), \] a state-feedback controller \(u=g(x)\) depends on knowledge of the state \(x\) which must be obtained from the measurement \(y\). An observer will determine an estimate \(\widehat x\) of the state which can be used in the control \(u=g(\widehat x)\). The question of when this can be done is called the separation principle. Using Lyapunov theory, this paper shows that such a principle exists for the above system under some mild conditions.