The Robust Stability Study For The Uncertain Nonlinear Systems With Time-delay

As we all know that nonlinear systems exist in the world extensively, time delays are inherent in systems and uncertainties are not avoidable. So it is important to investigate the robust stability analysis of uncertain nonlinear systems with time delays. Now it is one of the hotspots and also the difficulties in control domain. This paper summarizes some of theories of robust stability and based on the existing this, some work has been done in this paper on robust stability analysis and control of time-delay nonlinear systems.Firstly, On the basis of Lyapunov stability theories, The theorems of stability using the approach of linear matrix inequality and the principle of PDC and the concept of CDF (compensation and division for fuzzy model) are summarized in this paper and a kind of fuzzy controller which makes whole systems gradual stabilizing is got based on the T-S fuzzy dynamic model. I compare the above-mentioned methods and draw a conclusion after carefully analyzing. And the theorems of robust stability for uncertain continuous and discrete fuzzy nonlinear systems are summarized based on the T-S fuzzy dynamic model.Secondly, The fuzzy T-S model is used to approximate to time-delay nonlinear systems. And the sufficient condition of robust stability for time-delay nonlinear systems is put forward based on piecewise Lyapunov function and inequality method. In addition, a kind of fuzzy controller which makes whole systems stabilizing is designed in the paper.At last, the robust stability condition of time-delay nonlinear systems with two kinds of uncertain is summarized and a kind of fuzzy controller that makes the whole systems robust stability is introduced. At the same time, detailed illation of proof for this robust stability condition is put forward in the paper.