| Continuous Control-Lyapunov Functions for Asymptotically Controllable Time-Varying Systems (1997) | |||||||||||||||
Abstract | |||||||||||||||
| This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous control-Lyapunov function with respect to the set. 1 Introduction We will study continuous-time systems with dynamics given by di#erential equations of the type: x(t) = f(t, x(t), u(t)), (1) where x(t) # R n represents the state variable and u(t) # U is the control variable. (Technical assumptions on f and U are described below.) We are interested in questions of stabilization relative to a subset A of the state space R n . For example, the set A may be just an equilibrium point, or it may represent a target subset of a di#erent kind. This target set might be a desired periodic orbit, or, in the context of designing observers, the Equations (1) might represent a composite state x = (x 1 , x 2 ), consisting of the state x 1 of the original system together with the state x 2 of an observer; in that case,... | |||||||||||||||
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