Abstract
This paper proposes a Lyapunov method for estimating the asymptotic stability domain of polynomial discrete nonlinear systems. Based on an existing approach of attraction domain estimation for continuous nonlinear systems, we present an analogous technique focusing on discrete systems. The idea is to reformulate the problem as a bilinear matrix inequalities (BMI) optimization problem where the Lyapunov function is considered as a decision variable. The exploitation of polar coordinates and positive definite matrices properties defines the objective function and the constraint functions. One of the main advantages of this method is that the results are independent of the Lyapunov function. Furthermore, the obtained stability domain approaches the exact domain boundaries. An application example is illustrated to validate found results.
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