The vector-matrix Shulgin’s equations are used to stabilize the steady motions of mechanical systems with nonlinear geometric constraints in the case of incomplete information on the state. The momenta are introduced only for the cyclic coordinates that are not used to control. Three variants of the measurement vector are used to prove a theorem on the stabilization of control with the help of a part of the cyclic coordinates described by Lagrange variables. The control coefficients and the estimation system coefficients are specified by solving the corresponding Krasovskii linear-quadratic problem for a linear controlled subsystem without the critical variables corresponding to the redundant coordinates and to the introduced momenta. The stability of the complete closed nonlinear system is proved by reducing to a special Lyapunov case and by the application of the Malkin stability theorem in the case of time-varying perturbations.

中文翻译：

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具有冗余坐标的系统的稳定运动的稳定

在状态信息不完整的情况下，矢量矩阵Shulgin方程用于稳定具有非线性几何约束的机械系统的稳定运动。仅针对不用于控制的循环坐标引入矩量。测量矢量的三个变体被用于证明借助于Lagrange变量描述的一部分循环坐标来稳定控制的定理。通过求解线性控制子系统的相应Krasovskii线性二次问题，可以确定控制系数和估计系统系数，而该线性控制子系统没有与冗余坐标和引入的动量相对应的关键变量。