| Summary: | A series of problems of the time-lag system including robust stability analysis and guaranteed cost controller design are studied mainly based on the Lyapunov stability theory by linear matrix inequality method and time lag partitioning method in this paper. The time lag partitioning method is used to divide the whole time lag interval into N interval parts based on a new Lyapunov-Krasovskii functional for a class of uncertain time lag system in this chapter, besides, some free-weighting matrices are introduced to study time lag-dependent stability, for which sufficient conditions for time lag-dependent stability based on the linear matrix inequality, less conservative compared with previous results, are obtained. After that, by using the Lyapunov stability theorem & linear matrix inequality and combining with the time lag partitioning method to discuss analysis and design of robust H∞ controller for a class of the Lurie time-lag with existential state and control input at the same time, conditions for asymptotic stability based on linear matrix inequality and with H∞ performance are obtained and a design method for H∞ control law with systematic memory state feedback is given. Finally, a simulation example is given to illustrate effectiveness of the proposed method.
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