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Stability analysis and control of Lur'e singularly perturbed uncertain systems

In this paper, the absolute stability and feedback control problems of Lur'e singularly perturbed uncertain systems are investigated. An ε-dependent Lyapunov function is constructed. Using the Lyapunov theory and Linear Matrix Inequalities (LMIs) technique, the conditions of absolute stability of the system without disturbances are derived. Then, a method of designing feedback controller is developed which can guarantee the absolute stability of the Lur'e singularly perturbed uncertain systems. A numerical example is given to show the effectiveness of the criteria.