Asymptotic stability for time-variant systems and observability: Uniform and nonuniform criteria
- 147 Downloads
This paper presents some new criteria for uniform and nonuniform asymptotic stability of equilibria for time-variant differential equations and this within a Lyapunov approach. The stability criteria are formulated in terms of certain observability conditions with the output derived from the Lyapunov function. For some classes of systems, this system theoretic interpretation proves to be fruitful since—after establishing the invariance of observability under output injection—this enables us to check the stability criteria on a simpler system. This procedure is illustrated for some classical examples.
Key wordsControl systems Differential equations Time-variance Observability Asymptotic stability Circle criterion
Unable to display preview. Download preview PDF.
- [A1] Aeyels, D., Stability of nonautonomous systems by Liapunov's direct method, inGeometry in Nonlinear Control and Differential Inclusions, B. Jakubczyk, W. Respondek, and T. Rzezuchowski, eds., Polish Academy of Sciences, Institute of Mathematics, Banach Center Publications, vol. 32, 1995, pp. 9–17.Google Scholar
- [A3] Anderson, B. D. O., Exponential stability of linear equations arising in adaptive identification.IEEE Transactions on Automatic Control, vol. 22, 1977, pp. 84–88.Google Scholar
- [H] Hermes, H., Discontinuous vector fields and feedback control, inDifferential Equations and Dynamical Systems, J. K. Hale and J. P. LaSalle, eds., Academic Press, New York, 1967, pp. 155–165.Google Scholar
- [S] Sepulchre, R., Contributions to nonlinear control systems analysis by means of the direct method of Lyapunov, Ph.D. Dissertation, Université Catholique de Louvain, September 1994.Google Scholar