he variable t is usually referred to as the\time Note the use of an integral form in the formal definition(2.2): it assumes that the function tHa(a(t), t)is integrable on T, but does not require =a(t)to be differentiable at any particular point, which turns out to be convenient for working with discontinuous

Definition A real-valued function V: X H R defined on state space X of a system with behavior set B and state r:B×[0,∞)→ X is called a Lyapunov function if tHv(t)=v(a(t))=v(a(z(), t)) is a non-increasing function of time for every z E B according to this definition, Lyapunov

In particular, when o=0, this yields the definition of a Lyapunov function Finding, for a given supply rate, a valid storage function(or at least proving that one exists)is a major challenge in constructive analysis of nonlinear systems. The most com-

This lecture presents results describing the relation between existence of Lyapunov or storage functions and stability of dynamical systems 6.1 Stability of an equilibria

where f:R\×Rn×R→ R\ and g:R\×R\×R→ R are continuous functions. Assume that f, g are continuously differentiable with respect to their first two arguments in a neigborhood of the trajectory co(t), yo(t), and that the derivative

Lyapunov analysis, which uses monotonicity of a given function of system state along trajectories of a given dynamical system, is a major tool of nonlinear system analysis It is possible, however, to use monotonicity of volumes of subsets of the state space to predict certain properties of system behavior. This lecture gives an introduction to suc methods

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Lecture #4 16.61 Aerospace Dynamics Extension to multiple intermediate frames(two) Copyright 2002 by Jonathan How

航摄像片的基本知识 Basic Knowledge of aerial photos 航摄像片的判读 The Mapping of Relief Map  像片的立体观察 Solid observation of photos 航测资料在水利工程中的应用  Applying data of aerial survey in Irrigation Projects 航测成图的简要过程  The brief process of aerial survey 卫星像片简介  Brief introduction of aerial photos