Abstract

The hybrid affine system considered in the paper comes to existence when applying an impulse control of special form to the chain of four integrators. The goal of the control is to stabilize the system at the origin such that it approaches the equilibrium state along a given (desired) trajectory. The target trajectory is defined implicitly as that of the second-order integrator stabilized by means of a feedback in the form of nested saturators. The purpose of the study is to determine the range of the feedback coefficients for which this system is globally stable. The problem is shown to reduce to a simpler task of establishing stability of a second-order switched linear system with state-dependent switching law. It is proved that the latter system is stable for arbitrary switchings.

中文翻译：

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四阶混合仿射系统的全局稳定性

摘要

当对四个积分器链应用特殊形式的脉冲控制时，本文中考虑的混合仿射系统就出现了。控制的目标是使系统稳定在原点，使其沿着给定（期望）的轨迹接近平衡状态。目标轨迹隐式定义为通过嵌套饱和器形式的反馈稳定的二阶积分器的轨迹。研究的目的是确定该系统全局稳定的反馈系数范围。该问题被证明可以简化为一个更简单的任务，即建立具有状态相关切换律的二阶切换线性系统的稳定性。证明了后一个系统对于任意切换都是稳定的。