Lipschitz广义非线性系统观测器设计

研究一类广义非线性系统的观测器设计问题．首先讨论了半正定Lyapunov函数下指数1广义非线性系统稳定及渐近稳定性,然后对一类由线性和Lipschitz非线性项组成的广义非线性系统,给出了渐近稳定观测器存在的条件,并把观测器反馈增益矩阵的设计归结为广义线性系统容许控制以及奇异值计算问题,证明了若容许广义线性系统矩阵的最小奇异值大于系统的Lipschitz常数,容许控制器增益矩阵就是待求的观测器反馈增益矩阵。

Observer design for Lipschitz nonlinear singular systems

The observer design for nonlinear singular systems is discussed.First,for an index-one nonlinear singular systems,the stability and asymptotical stability with positive semi-definite Lyapunov functions are analyzed.Then,for nonlinear singular systems composed of linear and Lipschitz nonlinear terms,some sufficient conditions are proposed for the existence of asymptotically stable observer system.An algorithm is developed to calculate the observer gain,converting the original problem into admissible control of a linear singular system and the calculation of minimum singular value of the correspondingly closed system.It is proven that if the minimum singular value is greater than the Lipschitz constant of the nonlinear singular system,the admissible controller gain can serve as the observer gain.