一类符号反对称结构系统的稳定性及其应用

Stability of a Class of Systems with Sign-skew Symmetric Structure and Its Applications

结合矩阵论中的可反对称条件,提出一种稳定的具有符号反对称结构的系统,并将其作为非线性系统的镇定控制目标.面向符号反对称结构系统的控制方法存在递推构造法和直接设计方法两种:递推构造法面向具有上三角结构的系统,包括已有逆推控制和逆推自适应控制,并可具有更多的可调参数;直接设计法适用于低维系统,对于一些系统可以设计出更简单的控制器.对于Lorenz混沌同步系统的仿真说明了面向反对称结构系统直接设计法有效性.

Combined with skew-symmetrization condition in matrix theory, a class of stable systems with sign-skew symmetric structure is proposed, and is regarded as the objective of controller design. There are two methods to implement the design. One is called the direct method, in which the origin systems are transformed into systems with sign-skew symmetric structure by controller design and controllers simpler than backstepping for some systems can be constructed. Another is the recursive method, which is suitable for the systems with lower triangular structure, may have more parameters to tune than traditional backstepping procedure, and includes the backstepping and adaptive backstepping design procedures. An example of Lorenz systems is presented to show the effectiveness of the direct design method based on the sign-skew symmetric structure.