论文信息 - New converse Lyapunov theorems and related results on exponential stability

New converse Lyapunov theorems and related results on exponential stability

We treat the problem of constructing Lyapunov functions for systems which are, by assumption, exponentially stable. The construction we present results in a larger set of functions than those obtainable by previously known methods. A useful property of the proposed Lyapunov functions is that they preserve information on the rate of exponential convergence of the system. Some useful applications are given.

Luigi Glielmo | Martin Corless | M. Corless | L. Glielmo

[1] E. Coddington,et al. Theory of Ordinary Differential Equations , 1955 .

[2] M. Corless,et al. On the exponential stability of singularly perturbed systems , 1992 .

[3] Eduardo D. Sontag,et al. Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[4] R. A. DeCarlo. Linear Systems: A State Variable Approach With Numerical Implementation , 1989 .

[5] J. Dieudonne. Foundations of Modern Analysis , 1969 .

[6] R. E. Kalman,et al. Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems , 1960 .

[7] P. Hartman. Ordinary Differential Equations , 1965 .

[8] Yuandan Lin,et al. A Smooth Converse Lyapunov Theorem for Robust Stability , 1996 .

[9] Gene H. Golub,et al. Matrix computations , 1983 .

[10] T. H. Gronwall. Note on the Derivatives with Respect to a Parameter of the Solutions of a System of Differential Equations , 1919 .

[11] G. Leitmann,et al. Controller Design for Uncertain Systems via Lyapunov Functions , 1988, 1988 American Control Conference.

[12] W. Walter. Differential and Integral Inequalities , 1970 .

[13] Robert Bartle,et al. The Elements of Real Analysis , 1977, The Mathematical Gazette.

[14] Wolfgang Hahn,et al. Stability of Motion , 1967 .