Relative Controllability of Linear Difference Equations
Relative Controllability of Linear Difference Equations
复制标题
线性差分方程的相对可控性
DOI：
10.1137/16m1073157
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Guilherme Mazanti
中科院分区：
文献类型：
--
作者：
Guilherme Mazanti
In this paper, we study the relative controllability of linear difference equations with multiple delays in the state by using a suitable formula for the solutions of such systems in terms of their initial conditions, their control inputs, and some matrix-valued coefficients obtained recursively from the matrices defining the system. Thanks to such formula, we characterize relative controllability in time T in terms of an algebraic property of the matrix-valued coefficients, which reduces to the usual Kalman controllability criterion in the case of a single delay. Relative controllability is studied for solutions in the set of all functions and in the function spaces Lp and Ck. We also compare the relative controllability of the system for different delays in terms of their rational dependence structure, proving that relative controllability for some delays implies relative controllability for all delays that are “less rationally dependent” than the original ones, in a sense that we make precise. Finally, we provide an upper bound on the minimal controllability time for a system depending only on its dimension and on its largest delay.
