Showing papers on "Control-Lyapunov function published in 1971"
TL;DR: In this paper, the problem of automatically constructing a quadratic Lyapunov function V = x'Ax for a high order non-linear system given by x@? = f(x), f(0) = 0, where f is a continuous function of x which guarantees uniqueness of solutions of the system is dealt with.
188 citations
TL;DR: In this article, it was shown that a state space realization of an input-output stable dynamical system is globally asymptotically stable in the sense of Lyapunov if it is uniformly observable and if every state is reachable.
Abstract: This paper discusses the relationship between properties of input-output descriptions and state space models for dynamical systems. It is shown that a state space realization of an input-output stable dynamical system is globally asymptotically stable in the sense of Lyapunov if it is uniformly observable and if every state is reachable. This result is proved in the context of abstract dynamical systems and leads to the equivalence of input-output stability and asymptotic stability for uniformly controllable and uniformly observable linear finite-dimensional systems. The generation of Lyapunov functions is subsequently considered, and variational techniques for the construction of Lyapunov functions are presented. Passivity and related energy concepts are particularly exploited in this context. These results yield the Lyapunov functions used in the proofs of the circle criterion and the Popov criterion as particular cases. The generality of the approach, however, makes these ideas applicable to much more ...
115 citations
TL;DR: The direct method of Lyapunov applied to the problem of transient power system stability is developed to permit the practical study of n-machine systems and several ideas for a further generalization and optimization of the method and a possibility for the design and control of power systems are proposed.
Abstract: The direct method of Lyapunov applied to the problem of transient power system stability is developed to permit the practical study of n-machine systems. A simple physical interpretation and a proof are given for two Lyapunov functions. A new and better Lyapunov function is defined, and several possibilities for its evaluation are studied. Through an analysis of the singular points of the system the causes of the conservativeness of the results are established, and a further improvement on the Lyapunov function is made. A general structure for a computer program is proposed, and results of an example with a 10-machine system solved by the conventional and the new methods are presented; the computing time by the Lyapunov method was about 40-percent shorter. Finally, several ideas for a further generalization and optimization of the method and a possibility for the design and control of power systems are proposed.
45 citations
01 Mar 1971
TL;DR: In this paper, a new situation has been considered where vector Lyapunov functions play a further useful role and a new type of stability, namely, strict partial stability has been defined.
Abstract: It has been proved that the use of a vector Lyapunov function is more advantageous in certain situations rather than a scalar function. Moreover, each function needs to satisfy less rigid requirements. In this paper a new situation has been considered where vector Lyapunov functions play a further useful role. For this purpose, a new type of stability, namely, strict partial stability has been defined. The principal tool employed is the second method of Lyapunov and a comparision theorem of a more general type.
29 citations
TL;DR: In this paper, the Lyapunov operator corresponding to a stable system is described in terms of its mapping of the set of positive definite matrices, and its image is shown to have geometrical descriptions which simplify the analysis.
Abstract: In this paper, the Lyapunov operator corresponding to a stable system is described in terms of its mapping of the set of positive definite matrices. This set and its image are shown to have geometrical descriptions which simplify the analysis. This geometrical approach also yields a method for finding the ‘best’ Lyapunov function of the quadratic type for a system with a variable parameter
1 citations