输入有界线性离散系统可控区域的一种有效算法

针对输入有界的离散时间线性定常系统，利用凸多面体集合的几何特性，求解与有限步可控区域相联系的凸多面体集合的边界超平面法向量，进而得到有限步可控区域的精确表示，计算实践表明，与求解可控区域的传统方法相比，该方法具有更高的计算效率，且当有限步可控区域对应较多的步数时，该方法在计算效率上的优势更加显著．还结合最小时间控制问题和镇定问题，说明用该方法得到的有限步可控区域的精确描述，能够为解决约束系统的控制问题提供重要依据。

Efficient Algorithm for Computation of Controllable Region of Linear Discrete-Time Systems with Bounded Input

Based on the geometric properties of the hyperplanes that form the boundaries of a convex polytope, an efficient algorithm is presented to determine the exact finite-step controllable state set of linear discrete-time systems with input saturation. The key point is to directly obtain the norm of each hyperplane associated with finite-step controllable state set. The algorithm demonstrates higher computational efficiency than the traditional methods, particularly when the specified step is large enough. Moreover, minimum-time control problem and stabilization problem are also discussed to show that the exact characterization of the finite-step controllable regions via the approach can provide basis for solving control problem of constrained systems.