The Research On New Methods For Robustness Of Time-Delay Systems With Nonlinear Perturbation

When establishing models for practical control systems, there are errors, which can be described as the model uncertainties, between the systemic model and the practical problems because measurement errors, various disturbances and unestablished model dynamics are inevitable. In addition, states in many systems are not only relevant to the current system circumstances but also to some previous system circumstances, which can be called the time-delay of a system. Uncertainty and time-delay are important factors which affect the performance of a system. Therefore, research on uncertain time-delay systems is always an important and difficult part in the research on the problems of system control. Especially, the research has importantly theoretical significance and practical value if the uncertainties of systems have nonlinear feature.In this paper, new methods for robustness analysis of time-delay systems with nonlinear uncertainty are studied, in the case that the system has general nonlinear uncertainty.First, based on the traditional Lyapunov method, some new delay-dependent stabilization criterions are obtained by constructing appropriate Lyapunov-Krasovsk functionals and by applying relevant inequalities. These criteria, whose conservations are compared through numerical calculation by constructing numerical examples, are described in terms of linear matrix inequalities. According to the criteria we obtained, relevant state feedback controllers are designed. The controller gains are given by LMI and their availabilities are verified by numerical examples.Second, based on the traditional Lyapunov stability theory, some new criteria for robust stability of time-delay systems are obtained by discussing the system's robustness by means of three methods, including free weighing matrix approach, parametrized neutral model transformation method and descriptor model transformation method. These criteria are given in the form of LMI, and their allowable time-delay bounds are improved. First, free weighing matrix approach does not enlarge Lyapunov function derivation but introduces some identities that combine with Lyapunov function derivation and obtains stability conditions through calculation in the corresponding process. Second, parametrized neutral model transformation method transforms the original system into a new the system by allowing an operator with free matrix and obtains stability criteria for the original system by studying the stability of new system. Finally, descriptor model transformation method makes transformation for system, constructs augmented system and obtains the relevant stability conditions for original system according to the stability of augmented system. Similarly, based on these stability conditions, a series of state feedback controllers are designed and controller gains are described by relevant LMIs. Furthermore, it is shown by numerical examples that the conservation of the stability criteria we obtained is decreased and the design of state feedback controllers is feasible.