Delay-dependent Stability Analysis For Neutral Systems

The phenomenon with time-delays is frequently encountered in real world. The existence of the time-delay destroys the stability of systems and results in poor control performance severely. Meanwhile, following the development of science and technology, it is almost impossible to obtain accurate mathematics models for the object systems due to the complex dynamical behaviors and upper control request in the practical control process, which makes the stability analysis much more complicated. The stability is not only basic demand of the dynamical system, but also necessary precondition of keeping system in gear. So the exigent question in the design and application of real control systems, makes the stability analysis and research to become a hotspot and attract more and more researchers.The neutral systems contain not only information of the current state, but also the information of the past state and the derivative of the past state. Generally, we use the differential function of neutral type to depict these systems. The complexity of the performance in these functions keys makes more difficult in neutral systems analysis than time-delays systems analysis. So the development of the research on most of these systems is slow and we get little research fruit, except of the basic theory, the stability theory and the controllable theory. However, because a great number of time-delays systems can be translated into neutral systems. In the past twenty years, many people have paid attention on the stability analysis of time-delay neutral systems and achieved many results.By using the Lyapunov second method, combining with Leibniz-Newton formula, introducing into some suitable free-weight matrixes, considering the information contained in the system equation itself, adding some appropriate zero terms, recurring to LMI toolbox in MATLAB, this paper studies the problem of delay-dependent stability criteria for time- delay neutral systems, and gets some new stability criterion. The main works as following:1: The problems of delay-dependent stability criteria for a class of constant time-delay neutral systems are studied. It contains the stability criteria for invariable coefficient time-delay neutral systems, the stability criteria for constant time-varying neutral systems with time-varying structured uncertainties and the stability criteria for constant time-delay neutral systems with nonlinear perturbations. By considering the information contains in the system equation itself, employing some appropriate free-weight matrix, we got the delay-dependent stability criteria for the above systems, which had less conservative than the existing results.2: The discrete delay-dependent and neutral delay-independent stability criteria for time-varying time-delay neutral systems are discussed. The main study contain the stability criteria for invariable coefficient time-varying discrete time-delay neutral systems, the stability criteria for time-varying discrete time-delays neutral systems with time-varying structured uncertainties and the stability criteria for time-varying discrete time-delays neutral systems with nonlinear perturbations. By constructing appropriate Lyapunov functions, adding some appropriate zero terms into system equation, some sufficient conditions for discrete delay- dependent and neutral delay-independent stability are derived in the terms of the solutions of linear matrix inequality. Comparing with previous results by some numerical examples, the results are effective and less conservative than the previous conclusion.3: The delay-dependent robust stability for the neutral systems with multiple time-delays is investigated. First, a new delay-dependent stability criterion for two time delays is derived by considering the relationships amongτ_i(i= 1,2,…,m). A numerical example is presented to illustrate that the new sufficient condition is less conservative than the previous results. Finally, this idea is extended to neutral system with multiple time-delays.At last, we sum up all the paper and give some expectations of the stability study and controllability condition study for the time-delay neutral systems.