Stability Analysis of Implicit Polynomial Systems

This technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters. A polynomial (with respect to the state and uncertain parameters) Lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction. The results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters. Numerical examples illustrate the effectiveness of the developed approach.