Generalization of the Lyapunov equation to nonlinear systems. (English) Zbl 0643.93047
Summary: The Lyapunov equation for the characterization of the stability of linear systems is generalized to nonlinear systems.
MSC:
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 15A24 | Matrix equations and identities |
| 93C10 | Nonlinear systems in control theory |
| 15A72 | Vector and tensor algebra, theory of invariants |
| 34D20 | Stability of solutions to ordinary differential equations |
| 93C15 | Control/observation systems governed by ordinary differential equations |
References:
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| [2] | BANKS S. P., Syst. Control Lett. 5 pp 337– (1986) · Zbl 0582.93030 · doi:10.1016/0167-6911(86)90129-5 |
| [3] | BANKS S. P., Syst. Control Lett. 5 pp 327– (1985) · Zbl 0573.93026 · doi:10.1016/0167-6911(85)90030-1 |
| [4] | BROCKETT R. W., Proc. Inst, elect, electron. Engrs 64 pp 61– (1978) · doi:10.1109/PROC.1976.10067 |
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| [6] | LOPARA K. A., I.E.E.E. Trans, autom. Control 23 pp 602– (1978) · Zbl 0385.93023 · doi:10.1109/TAC.1978.1101779 |
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