Stability Analysis For Nonlinear Systems And Swarm-Robot Formation Control Based On Stability

Systems engineering is a technology for analyzing and designing systems based on the aims of systems. Stability, one of the most essential and the most important properties of systems, has to be considered in any system analysis and design, so it is a significant subject in systems engineering.Among all methods for analyzing stability, because of its special advantages and wide applications, the Liapunov direct method has turned into the most important and the most essential method. However, when the Liapunov direct method is used, a Liapunov function must be constructed. For linear systems, this problem has been solved, but for nonlinear systems, the problem still exist, so it is still very difficult to test a nonlinear system's stability. Consequently study of the approaches for constructing nonlinear systems' Liapunov functions is of interest, and much work has been done for this subject in this paper firstly.For swarm-robot formation control, a useful and challengeable subject, stability is one of principal aims in its control system design. However although many methods have been produced for formation control, they are all not general and efficient enough, and some of them even don't have stability, so it is of use to design a control system for formation control based on stability, and much work also has been done for this subject in this paper.The main contributions, for nonlinear stability analysis, are the following.Firstly, some new conceptions such as component function matrix and generalized quadratic form function are presented. Some criteria for the definite-sign property of generalized quadratic form function, diagonal-friend component function matrix and analogy two-element component function matrix are derived. The steps used to resolve an ordinary symmetrical component function matrix into the addition of diagonal-friend component function matrices are also given.Secondly, the conception coefficient element function matrix is defined and some important theorems are proofed. Based on above results, a new method named generalized quadratic form method is proposed for Liapunov...