- ▪L. Wang, P. de Leenheer, E.D. Sontag, "Conditions for global stability of monotone tridiagonal systems with negative feedback", Systems and Control Letters, vol. 59, pp. 138-130, 2010. pdf
Abstract
This paper studies monotone tridiagonal systems with negative feedback. These systems possess the Poincaré-Bendixson property, which implies that, if orbits are bounded, if there is a unique steady state and this unique equilibrium is asymptotically stable, and if one can rule out periodic orbits, then the steady state is globally asymptotically stable. Different approaches are discussed to rule out period orbits. One is based on direct linearization, while the other uses the theory of second additive compound matrices. Among the examples that will illustrate our main theoretical results is the classical Goldbeter model of circadian rhythms.
- ▪L. Wang, P. de Leenheer, E.D. Sontag, "Global stability for monotone tridiagonal systems with negative feedback", In Proc. IEEE Conf. Decision and Control, Cancun, Dec. 2008, pp. 4091-4096, 2008.
Abstract
Conference version of paper "Conditions for global stability of monotone tridiagonal systems with negative feedback"
- ▪H.J. Sussmann, E.D. Sontag, Y. Yang, "A general result on the stabilization of linear systems using bounded controls", IEEE Trans. Automat. Control, vol. 39, no. 12, pp. 2411–2425, 1994. pdf
Abstract
We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a "neural-network type" one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations.