Research On Robust Stability For A Class Of 2-D Positive Systems

In recent years,with the rapid development of theoretical and applied research on multi-dimensional signals and systems,the research on positive systems has also evolved from one-dimensional to multi-dimensional,especially two-dimensional(2-D)positive systems.This paper studies the robust stability of discrete 2-D positive systems with interval uncertainty.The major work of research is as follows:First,the robust stability of discrete 2-D non-state-delayed positive systems with interval uncertainties is studied.According to the asymptotical stability criteria of the existing 2-D positive systems with non-state-delayed,a sufficient and necessary condition for the robust stability of 2-D non-state-delay positive systems with interval is established,and a robust feedback controller is designed.Second,the asymptotic stability of the 2-D positive systems with multiple state-delayed and the robust stability under the uncertainty of the interval are studied.Firstly,the 2-D positive systems with multiple state-delayed are transformed into 2-D non-state-delayed positive systems.Then the necessary and sufficient conditions for the asymptotical stability of the 2-D positive system with multiple state-delayed are given by using the asymptotical stability criteria of the existing 2-D positive systems without state-delayed.Finally,based on the obtained asymptotic stability criterion,a necessary and sufficient condition for the robust stability of 2-D positive systems with multiple state-delayed is deduced.Thirdly,the robust stability of 2-D discrete state-delayed positive systems using generalized Overflow Nonlinearities with interval uncertainties is studied.By the method of constructing the Lyapunov function,the robust stability criteria for a generalized overflow nonlinear 2-D positive systems with state-delayed is established.Based on this,a criterion for robust stability of a 2-D state-delayed positive systems with interval intervals is deduced.The conclusions above are given in the form of LMI,which make the calculation is convenient.And the validity of the conclusions is verified by numerical examples.