On Periodic Motion of Linear Systems with State Jump-Modelling, Stability Analysis and Feedback Control of Compass Walking
On Periodic Motion of Linear Systems with State Jump-Modelling, Stability Analysis and Feedback Control of Compass Walking
复制标题
线性系统周期运动的状态跳跃建模、稳定性分析和罗盘行走反馈控制
DOI：
10.5687/iscie.17.553
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
H. Kokame
中科院分区：
文献类型：
--
作者：
K. Hirata;H. Kokame
本文研究具有状态跳变的线性系统周期解的稳定性问题。该模型的通用性足以描述一类混合系统的复杂动力学，包括（近似的）双足被动罗盘行走，它也保留了分析数学处理的可追溯性。通过对稳定性的适当定义，我们可以证明庞加莱图在分析中的使用是合理的。给出了决定周期解局部稳定性的线性化庞加莱映射的公式。在已知标称轨迹的情况下，还讨论了反馈控制的效果。
In this paper, we consider the stability of periodic solution of linear systems with state jump. While this model is general enough to describe the complex dynamics of a class of hybrid systems including the (approximated) biped passive compass walking, it also retains the tractability for the analytic mathematical treatment. With an appropriate definition of the stability, we can justify the use of Poincare map in the analysis. The formula for the linearized Poincare map, which determines the local stability of the periodic solution, is given. The effect of feedback control (for the case that the nominal trajectory is known) is also discussed.