This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delays.The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision.A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory.With the help of linear matrix inequality(LMI) method,robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive.Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate.A numerical example illustrates the validity of the proposed method.
The global stabilization of asymptotically null controllable linear systems by bounded control is considered. A nested type saturation control law is proposed which is a generalization of the existing results reported in the literature. The primary characteristic of this modified control law is that more design parameters,which are the closed-loop eigenvalues when the system is operating in linear form,are introduced and which can be well designed to achieve better system performance. Using this law,the pole locations of the closed-loop systems depending on a linear transformation can be placed arbitrarily within certain areas. Numerical example shows that the performance of the closed-loop system under this control law can be significantly improved if the free parameters are properly chosen.
To obtain a stable and proper linear filter to make the filtering error system robustly and strictly passive, the problem of full-order robust passive filtering for continuous-time polytopic uncertain time-delay systems was investigated. A criterion for the passivity of time-delay systems was firstly provided in terms of linear matrix inequalities (LMI). Then an LMI sufficient condition for the existence of a robust filter was established and a design procedure was proposed for this type of systems. A numerical example demonstrated the feasibility of the filtering design procedure.
