Balanced truncation of linear time-varying systems

Sandberg H.; Rantzer A.

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Balanced truncation of linear time-varying systems

机译：线性时变系统的平衡截断

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In this paper, balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case of time-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.

机译：本文研究了线性时变系统在离散和连续时间内的平衡截断。基于相对时变的Lyapunov方程/不等式的计算，我们能够得出截断模型的上下误差范围。这些结果归纳了众所周知的时不变公式。考虑时变状态维的情况。所有截断的平衡实现的输入输出稳定性也得到了证明。该方法最终成功地应用于高阶模型。

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《IEEE Transactions on Automatic Control》 |2004年第2期|p.217-229|共13页
作者
Sandberg H.; Rantzer A.;
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正文语种 eng
中图分类自动化系统;
关键词
Lyapunov matrix equations; continuous time systems; discrete time systems; input-output stability; invariance; linear systems; observability; reachability analysis; reduced order systems; time-varying systems; Lyapunov equations; Lyapunov inequalities; balanced trun;

机译：Lyapunov矩阵方程;连续时间系统;离散时间系统;输入输出稳定性;不变性;线性系统;可观测性;可达性分析;降阶系统;时变系统;Lyapunov方程;Lyapunov不等式;平衡截距;

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Balanced truncation of linear time-varying systems

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