Uniting two Control Lyapunov Functions for affine systems

Abstract : The problem of piecing together two Control Lyapunov Functions (CLFs) is addressed. The first CLF characterizes a local asymptotic controllability property toward the origin, whereas the second CLF is related to a global asymptotic controllability property with respect to a compact set. A sufficient condition is expressed to obtain an explicit solution. This sufficient condition is shown to be always satisfied for a linear second order controllable system. In a second part, it is shown how this uniting CLF problem can be used to solve the problem of piecing together two stabilizing control laws. Finally, this framework is applied on a numerical example to improve local performance of a globally stabilizing state feedback.
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IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2010, 55 (8), pp.1923-1927
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Vincent Andrieu, Christophe Prieur. Uniting two Control Lyapunov Functions for affine systems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2010, 55 (8), pp.1923-1927. 〈hal-00552094〉

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