Analysis And Synthesis Of Time-delay Nonlinear Singular Systems

Singular systems have been widely used in lots of disciplines such as robots, electronic network, aerospace, economics management and biomedical etc. There are some results on singular systems, but most of them limits to linear systems, and less amount of literature study the nonlinear singular systems. The main problem is the existence of solution for nonlinear singular systems still not resolved. In addition, there widespread exist delays in actual systems because of information transmission and processing. The existence of the delays can lead to unstability of the control systems and the degradation of the performance. The theory of time-delay singular control systems is not perfert and it has been rarely reported both in domestic and abroad. So, whether it is for the improvement and development of the theoretical system, or in order to apply theory to parctice as soon as possible, researches on time-delay nonlinear systems are very necessery, both the contents and methods are urgently need to innovation, development and systematic.The primary task of this paper is to solve the existence and uniqueness of solution and its stability for time-delay nonlinear singular systems by functional analysis. On that basis, this paper also study the H_∞reliable tracking control peoblem and the observer design for singularly perturbed systems, give new theoretical results, enrich and improve the theoretical system, and add new content and background of singular system theory. The main contents and research results of this paper include the following aspects:1. The existence and uniqueness of solution and its stability for discrete-time nonlinear descriptor systems with time-delay is discussed. Firstly, by means of fixed point principle, a matrix inequality criterion is presented which guarantees the existence and uniqueness of solution. Then secondly, the existence and uniqueness of solution is also proved via linear matrix inequality. Thirdly, the solution is proved to be globally exponentially stable via this linear matrix inequality, which means a sufficient condition is presented such that the discrete-time descriptor nonlinear systems with time-delay is globally exponentially stable. In addition, it is easy to verify that the criterion presented is independent of the choices of decomposition matrices for the given system. Finally, the approach is illustrated by a numerical example.2. H_∞reliable tracking control for continuous-time nonlinear singular systems with time-delay is considered. Considering both actuator failures and sensor failures, a sufficient condition is given such that the closed-loop system is regular, impulse free and exponentially stable, and the system output tracks the given reference model output and satisfies H_∞performance. Then, corresponding reliable controllers are designed respectively by means of linear matrix inequalities technique. Furthermore, an illustrative numerical example is presented to show the effectiveness of the proposed approach.3. The existence and uniqueness of solution and its stability and the observer design for continuous-time nonlinear singularly perturbed systems with time-delay is studied, and the nonlinear functions in the systems satisfy the Lipschitz condition. Firstly, by means of fixed point principle, a sufficient condition is presented such that the solution of the system is exist and unique. Then secondly, based on Lyapunov stability theory, a Luenberger state observer with the singular perturbation parameter is designed and the existence condition of the observer is given in terms of linear matrix inequality. Finally, an illustrative numerical example is presented to show the effectiveness of the proposed approach.