Showing papers on "Control-Lyapunov function published in 1977"
47 citations
01 Dec 1977
TL;DR: In this paper, the Lagrange's function is used to estimate the critical reclosing time for power-system transient stability, which is then compared with those obtained by numerical integration, and numerical results are shown.
Abstract: A systematic procedure of constructing Lyapunov functions for power systems is considered. A new approach is presented, which uses a construction technique of the Lagrange's function resulting from 2nd-order ordinary differential equations. The application of this new method to power-system transient-stability problems is illustrated by considering a single-machine system, taking into account the effect of the velocity governor, which is represented by 1st-order or 2nd-order response. The Lyapunov functions may then be used to estimate the critical reclosing time for power-system transient stability. The critical reclosing times given by these Lyapunov functions are compared with those obtained by numerical integration, and numerical results are shown. Further-more, it is discussed how a Lyapunov function indicates the relative effects of control-system parameters on the stability characteristic of a generator.
26 citations
3 citations
01 Dec 1977
TL;DR: In this paper, the authors compared analysis methods of large scale systems by scalar Lyapunov functions (SLF) and vector LyAPF (VLP) and showed that for most systems considered in the literature, the vector LFF approach reduces to the scalar LFL approach.
Abstract: Analysis methods of large scale systems by scalar Lyapunov functions and vector Lyapunov functions are contrasted. It is shown that for most systems considered in the literature (a) the vector Lyapunov function approach reduces to the scalar Lyapunov function approach, and (b) the scalar Lyapunov function approach, when applied to these systems, can yield less conservative results than the vector Lyapunov function approach.
1 citations
TL;DR: In this paper, it was shown that for continuous strong Markov processes, there exists a Lyapunov function which satisfies an exponential inequality along the process, and this is also true for discrete-time processes.
Abstract: If a continuous strong Markov process is exponentially stable w.p.l., then there exists a Lyapunov function which satisfies an exponential inequality along the process. An analogous result is also true for discrete-time processes, but requires a different construction for the Lyapunov function. This is in contrast to the case of asymptotic stability w.p.l. for which the same construction is valid for both continuous and discrete-time processes.