This paper deals with the state feedback control for linear systems in the presence of state delay using a direct numerical design methodology. The design algorithm iteratively searches the solution space of controller parameters to find a proper controller gain that guarantees the delay-independent stability of the closed-loop system. The algorithm divides the solution space to some simplexes, selects one simplex and evaluates two checking methods on this simplex. The first method checks the stabilisability of the corner points (to establish the feasible point) and the other detects the total infeasibility (total de-stabilisability) of the simplex (to omit the undesired parts). One interesting property of the method is its capability in detecting total de-stabilisability of a simplex through its corner points. If none of these methods is successful, the simplex is divided into two smaller ones which will be checked in the next algorithm’s iterations. According to the direct search nature, the algorithm is non-conservative and assuredly reaches a stabilizable point in the feasible space of the design space. The proposed algorithm and previous methods are evaluated on a set of random generated systems to compare the feasibility of the methods. Simulation results reveal the superiority of the proposed algorithm.

本文使用直接数值设计方法处理存在状态延迟的线性系统的状态反馈控制。设计算法迭代搜索控制器参数的解空间以找到合适的控制器增益，以保证闭环系统的延迟无关稳定性。该算法将解空间划分为一些单纯形，选择一个单纯形并在该单纯形上评估两种检查方法。第一种方法检查角点的稳定性（以建立可行点），另一种方法检测单纯形的总不可行性（total de-stabilsability）（忽略不需要的部分）。该方法的一个有趣特性是它能够通过其角点检测单纯形的整体不稳定。如果这些方法均不成功，则将单纯形分成两个较小的，将在下一个算法的迭代中进行检查。根据直接搜索的性质，该算法是非保守的，并且在设计空间的可行空间中肯定会达到一个稳定点。所提出的算法和以前的方法在一组随机生成的系统上进行评估，以比较这些方法的可行性。仿真结果表明了该算法的优越性。所提出的算法和以前的方法在一组随机生成的系统上进行评估，以比较这些方法的可行性。仿真结果表明了该算法的优越性。所提出的算法和以前的方法在一组随机生成的系统上进行评估，以比较这些方法的可行性。仿真结果表明了该算法的优越性。