Systems & Control Letters
Nonquadratic Lyapunov functions for robust control
Automatica (Journal of IFAC)
Piecewise Lyapunov functions for robust stability of linear time-varying systems
Systems & Control Letters
Automatica (Journal of IFAC)
Brief Homogeneous Lyapunov functions for systems with structured uncertainties
Automatica (Journal of IFAC)
Analysis of linear systems using truncated ellipsoids
ACC'09 Proceedings of the 2009 conference on American Control Conference
ACC'09 Proceedings of the 2009 conference on American Control Conference
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Based on a recent duality theory for linear differential inclusions (LDIs), the condition for stability of an LDI in terms of one Lyapunov function can be easily derived from that in terms of its conjugate function. This paper uses a particular pair of conjugate functions, the convex hull of quadratics and the maximum of quadratics, for the purpose of estimating the domain of attraction for systems with saturation nonlinearities. To this end, the nonlinear system is locally transformed into a parametertized LDI system with an effective approach which enables optimization on the parameter of the LDI along with the optimization of the Lyapunov functions. The optimization problems are derived for both the convex hull and the max functions, and the domain of attraction is estimated with both the convex hull of ellipsoids and the intersection of ellipsoids. A numerical example demonstrates the effectiveness of this paper's methods.