发表机构
Universidade de Santiago de Compostela; CITMAga（圣地亚哥-德孔波斯特拉大学; 计算数学与技术应用中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究线性Stieltjes微分系统的可达性与精确可控性，构造演化族与变易公式，刻画可达子空间，给出Kalman条件充分必要条件，并分析纯原子测度下的Krylov空间结构及能量行为。
AI 中文摘要
我们研究了由非递减左连续Stieltjes导数驱动的系统的可达性与精确可控性，该导数的测度可能包含连续部分、奇异连续部分和原子部分，而平坦区间表示系统不活动。我们构造了一个演化族和跳跃后的常数变易公式，并将可达子空间刻画为输入方向的基本张成。对于常系数情形，Kalman条件对每个导数都是必要的，并且在回归性假设下，当导数在某个子区间上连续且非恒定时，该条件也是充分的。若测度为纯原子且恰好有$N$个正原子，则可达子空间是由$B,AB,\ldots,A^{N-1}B$生成的截断Krylov空间；对于Kalman可控对，纯原子导数中最小原子数等于可控性指标。在阈值数量处，一个质量趋零而其余质量收敛到正有限极限会导致Gramian退化及最坏情况能量爆炸；在阈值或以上，紧致正质量范围产生一致强制性。一个混合双积分器示例说明了这些结果。
英文摘要
We study reachability and exact controllability for systems driven by a nondecreasing left-continuous Stieltjes derivator whose measure may have continuous, singular-continuous and atomic parts, while flat intervals represent inactivity. We construct an evolution family and post-jump variation-of-constants formula, and characterize the reachable subspace as the essential span of input directions. For constant coefficients, the Kalman condition is necessary for every derivator and, under regressivity, sufficient when the derivator is continuous and nonconstant on a subinterval. If the measure is purely atomic with exactly $N$ positive atoms, the reachable subspace is the truncated Krylov space generated by $B,AB,\ldots,A^{N-1}B$; for a Kalman-controllable pair, the minimum atom count among purely atomic derivators equals the controllability index. At the threshold count, one vanishing mass with the others converging to positive finite limits causes Gramian degeneration and worst-case energy blow-up; at or above threshold, compact positive mass ranges yield uniform coercivity. A mixed double-integrator example illustrates the results.
