IEEE Transactions on Automatic Control · 1992 · 133 citations · 10 references
Natural SciencesMathematicsSystems EngineeringDynamical SystemsProcess ControlSystem DynamicsContinuous Dynamical SystemsContinuous SystemsControl Of Dynamical SystemsControl SystemsControl TheoryStability TheoryLinear Control SystemsLyapunov ControlLyapunov FunctionsLyapunov StabilityLyapunov Stability TheoryLyapunov-based ControlMatrix NormsVector Norms
A unified theory of quadratic and piecewise-linear Lyapunov functions for continuous and discrete-time linear systems is presented. The key to this work is the description of these Lyapunov functions by vector norms. The main results are sufficient and necessary conditions for a vector norm to be a Lyapunov function as well as a method (based on these conditions) of constructing such Lyapunov functions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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