For differential equations with r parameters, 2r+1 experiments are enough for identification

Given a set of differential equations whose description involves unknown parameters, such as reaction constants in chemical kinetics, and supposing that one may at any time measure the values of some of the variables and possibly apply external inputs to help excite the system, how many experiments are sufficient in order to obtain all the information that is potentially available about the parameters? This paper shows that the best possible answer (assuming exact measurements) is 2r+1 experiments, where r is the number of parameters.Comment: This is a minor revision of the previously submitted report; a couple of typos have been fixed, and some comments and two new references have been added. Please see http://www.math.rutgers.edu/~sontag for related wor

Asymptotic amplitudes and cauchy gains: A small-gain principle and an application to inhibitory biological feedback

The notions of asymptotic amplitude for signals, and Cauchy gain for input/output systems, and an associated small-gain principle, are introduced. These concepts allow the consideration of systems with multiple, and possibly feedback-dependent, steady states. A Lyapunov-like characterization allows the computation of gains for state-space systems, and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops. An application in biology (MAPK signaling) is worked out in detail.Comment: Updates and replaces math.OC/0112021 See http://www.math.rutgers.edu/~sontag/ for related wor