Number characteristics of observability for nonlinear continuous-time control systems (Q2703078)

Nonlinear, continuous-time, finite-dimensional control systems with constant coefficients are considered. Using methods of differential geometry, observability properties of analytic control systems are investigated. It is shown that in the case of polynomial control systems there exists upper bounds for the number of iterated time derivatives of the output which are necessary to establish observability. Moreover, a procedure for testing the observability of polynomial control systems affine in the control is proposed. The role of the characteristics in observability problem is also discussed. Relations to observability results existing in the literature are also pointed out. Moreover, several remarks and comments on nonlinear, analytic and polynomial control systems are presented. Similar considerations concerning observability of nonlinear systems can be found in the paper [\textit{K. E. Starkov}, Autom. Remote Control 55, No. 12, Pt. 1, 1754-1761 (1994; Zbl 0854.93017)].