A new algorithm for computing higher-order approximate linearization of multi-input nonlinear control systems
一种新的多输入非线性控制系统高阶逼近线性化的计算方法

In practice, it is difficult to obtain a coordinate transformation and feedback to construct linear approximationfor nonlinear systems, even though the systems is approximate feedback linearizable. The reason is that it is necessary to solve a set of partial differential equations. In this paper, we firstly introduce an extended coordinate space and deduce a new matrix presentations for a general form of systems called linearly controllable muti-input nonlinear systems. Based on these preparations, we propose an effective construct algorithm procedure which leads to a computational reduction for obtaining a coordinate transformation and feedback. Finally we illustrate its application with the example of a dynamic feedback linearizablesystem.