Observer Design For Two Classes Of Nonlinear Time - Delay Systems With Triangular Form

In recent years, the study of nonlinear time-delay systems has become a hot topic in many engineering fields.Generally, the complexity of the system is caused by the uncertainty. A widespread attention has been devoted to the problem of stability and control analysis of time-delay systems.The basic technology on time delay problem are Lyapunov-Krasovskii and Lyapunov-Razumikhin methods, At the same time, with the development of deeply researching for nonlinear systems including unknown parameter or fault, good research achievements on adaptive control and state estimation for nonlinear system will have a broader space.The text mainly construct observers of two kinds of nonlinear time-delay systems. The two kinds of systems include wide uncertainties, for example, uncertain parameter, uncertain input coefficient, fault in dynamics of system, multiple time delays and so on. Under the assumption of the systems have triangular form, by state augmentation, the unknown parameter or the fault is seen as an extension of the system state, we construct asymptotic observers for nonlinear timedelay systems. Specifically, the paper mainly studied the following two parts:1. Adaptive observer design for a class of nonlinear time-delay systems with unknown parameter.In this part, adaptive observer design for a class of nonlinear time-delay systems with unknown parameter is solved. By state augmentation, with some mild conditions, the unknowninput coefficient is seen as an extension of the system state and consequently, an input-gain observer can be conceived to steer the observation error to the origin for some bounded and non-null control input. With the simultaneous state and parameter estimation, guarantees that the gain parameter γ converges to a reasonable fixed value. By using asymmetric saturation functions, we restrict the variation of the nonlinearity vector in the same range of variation of the system nonlinearity, and the observer gain is derived from a time-varyingparameter-dependent Ricaati equation with arbitrary weighting matrices.2. Nonlinear asymptotic observer design for a class of nonlinear multiple time-delay systems with fault.In this part, nonlinear asymptotic observer design for a class of nonlinear multiple timedelay systems with fault is solved. We assume the system has a triangular structure and the fault is a scalar and polynomial time-dependent function. Considering the augmented system, by fault reconstruction, and based on the Lyapunov analysis method, we design the asymptotic observer for unknown-input nonlinear time-delay systems satisfying the global Lipschitz condition. It addressed simultaneous state and fault estimation for the dynamics of system along with fault. It shows that the the observer gain is not related to any delaydependent condition.