A survey of extreme point results for robustness of control systems
Automatica (Journal of IFAC) - Special issue on robust control
Bibliography on robust control
Automatica (Journal of IFAC) - Special issue on robust control
Nonquadratic Lyapunov functions for robust control
Automatica (Journal of IFAC)
Brief On absolute stability analysis by polyhedral Lyapunov functions
Automatica (Journal of IFAC)
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In this paper we study the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties making use of piecewise linear (polyhedral) Lyapunov functions. A given class of Lyapunov functions is said to be "universal" for the uncertain system under consideration if the search of a Lyapunov function that proves the robust stability of the system can be restricted, without conservatism, to the elements of the class. In the literature it has been shown that the class of polyhedral functions is universal, while, for instance, the class of quadratic Lyapunov functions is not. This fact justifies the effort of developing efficient algorithms for the construction of optimal polyhedral Lyapunov functions. In this context, we provide a novel procedure that enables to construct, in the general n-dimensional case, a polyhedral Lyapunov function to prove the robust stability of a given system. Some numerical examples are included, where we show the effectiveness of the proposed approach comparing it with other approaches proposed in the literature.