A new methodology based on the linear matrix inequality (LMI) framework is presented for the computation of polynomial Lyapunov functions for differential–algebraic nonlinear systems. The method is applied for estimating the domain of attraction of equilibria and also as a control design tool to increase the damping of the system. Numerical examples are used to demonstrate the approach. The results show the potential of the proposed approach as a tool for analysis and control design.
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Coutinho et al. (2004) studied this question.
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