一类更一般Lipschitz非线性系统的观测器设计

研究了一类更一般Lipschitz非线性系统的观测器设计问题, 将渐近收敛观测器设计问题转化为求解相应的增益矩阵问题, 并给出了增益矩阵满足的充分条件和计算该增益矩阵的方法. 首先, 当系统满足某种可检测性时,利用奇异值理论得到了使得观测误差渐近收敛的增益矩阵需满足的充分性条件, 并基于Riccati方程给出了计算增益矩阵的方法. 其次, 当系统不满足该可检测性, 但满足其它条件时, 仍存在使得观测误差渐近收敛的增益矩阵, 并类似地得到了增益矩阵满足的充分性条件和计算方法. 仿真算例验证了该理论结果的正确性.

Observer design for a class of more general Lipschitz nonlinear systems

The observer design is investigated for a class of more general Lipschitz nonlinear systems.The problem of asymptotically convergent observer design is changed into solving the corresponding gain matrix.The sufficient conditions satisfied by the gain matrix are given,and the method of solving the gain matrix is also presented.First,under certain detectability that the system satisfies,the sufficient conditions are presented for the asymptotic convergence of the observer error by using the singular value theory.The method of solving the gain matrix is presented based on the Riccati equation.Second,when the system does not satisfy such detectability but satisfies other conditions,there is a gain matrix ensuring the asymptotic convergence of the observer error,and the sufficient conditions and the method of solving the gain matrix are similarly obtained.Two simulation examples are given to demonstrate the correctness of the theoretical results.