论文标题
无线尺寸非线性时间变化系统的积分输入到状态稳定性的表征
Characterization of integral input-to-state stability for nonlinear time-varying systems of infinite dimension
论文作者
论文摘要
对于大量的无限时间变化的控制系统，在零输入（0-GUA）（0-GUA）下，整体投入到国家稳定性（IISS）与全球均匀渐近稳定性的组合之间的等效性在合理的假设下是在较合理的范围内以均衡的方式建立的，该假设是在持续的范围内建立的。通过针对无限维系统的特定实例，例如时间延迟或在Banach空间上的半线性，可以根据定义动力学的功能给出足够的条件。此外，还表明，对于非线性术语满足状态规范绑定的半线性系统，ISS认为仅与0-GUA相当，这一事实是双线性系统所闻名的事实。另一个重要方面是，所考虑的IISS概念比标准概念更一般。
For large classes of infinite-dimensional time-varying control systems, the equivalence between integral input-to-state stability (iISS) and the combination of global uniform asymptotic stability under zero input (0-GUAS) and uniformly bounded-energy input/bounded state (UBEBS) is established under a reasonable assumption of continuity of the trajectories with respect to the input, at the zero input. By particularizing to specific instances of infinite-dimensional systems, such as time-delay, or semilinear over Banach spaces, sufficient conditions are given in terms of the functions defining the dynamics. In addition, it is also shown that for semilinear systems whose nonlinear term satisfies an affine-in-the-state norm bound, it holds that iISS becomes equivalent to just 0-GUAS, a fact known to hold for bilinear systems. An additional important aspect is that the iISS notion considered is more general than the standard one.
