1999/03/01 by F. Blanchini, Franco Blanchini, S. Miani +1 · 3 citations
Engineering · #Stability and Control of Uncertain Systems #Advanced Control Systems Optimization #Control Systems and Identification
paper · doi:10.1109/9.751368
The authors analyze the problem of synthesizing a state feedback control for the class of uncertain continuous-time linear systems affected by time-varying memoryless parametric uncertainties. They consider as candidate Lyapunov functions the elements of the class /spl Sigma//sub p//sup z/ which is formed by special homogeneous positive definite functions. They show that this class is universal in the sense that a Lyapunov function exists if and only if there exists a Lyapunov function in /spl Sigma//sub p//sup z/. They prove this result in a constructive way, showing that such a Lyapunov function can always be obtained by "smoothing" a polyhedral function for which construction algorithms are available. The authors show that unlike the polyhedral Lyapunov functions, these functions allow us to derive explicit formulas for the stabilizing controller.