Extension of the transfer function approach to the realization problem of nonlinear systems to discrete-time case
Extension of the transfer function approach to the realization problem of nonlinear systems to discrete-time case
复制标题
将非线性系统实现问题的传递函数方法扩展到离散时间情况
DOI：
10.3182/20100901-3-it-2016.00121
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Ü. Kotta
中科院分区：
文献类型：
--
作者：
M. Halás;Ü. Kotta
本文将非线性控制系统实现问题的多项式方法，即寻找由输入输出方程描述的SISO非线性系统的可观测状态空间表示的问题，推广到离散情况。为了找到解决方案，所谓的伴随多项式和伴随传递函数建立直接连接到已知的线性系统的解决方案。此外，在一个系统是不可实现的情况下，它示出，不同于在连续时间的情况下，总是存在一个postcompensator，当与串联连接的系统相结合，使补偿系统可实现。由于在组合系统时使用传递函数代数的可能性，这个问题可以以自然的方式解决。
Abstract In this paper the polynomial approach to the realization problem of nonlinear control systems, i.e. the problem of finding an observable state space representation of a SISO nonlinear system described by an input-output equation, is extended to the discrete-time case. To find the solution the so-called adjoint polynomials and adjoint transfer functions are employed establishing direct connection to the solution known from linear systems. In addition, in case a system is not realizable it is shown that, unlike in continuous-time case, there always exists a postcompensator which, when combined with the system in series connection, makes compensated system realizable. Due to the possibility to use the transfer function algebra when combining systems this problem can be solved in natural way.