In this paper, the finite-time non-fragile boundary feedback control problem is investigated for a class of nonlinear parabolic systems, where both the multiplicative and additive controller gain variations are considered to describe the actuator parameter perturbation. Non-fragile boundary control strategies are designed with respect to two controller gain variations via collocated or non-collocated boundary measurement, respectively. In light of the finite-time stability and Lyapunov-based techniques, some sufficient conditions are presented in terms of linear matrix inequalities such that the resulting closed-loop system is well-posedness and practically finite-time stable. Finally, numerical examples are given to verify the effectiveness of the proposed design method.

在本文中，研究了一类非线性抛物线系统的有限时间非脆弱边界反馈控制问题，其中考虑了乘性和相加控制器增益的变化来描述执行器参数的摄动。针对分别通过并置或非并置边界测量的两个控制器增益变化设计了非脆弱边界控制策略。根据有限时间稳定性和基于Lyapunov的技术，就线性矩阵不等式提出了一些充分的条件，从而使所得的闭环系统具有良好的适定性并且实际上是有限时间稳定的。最后，通过数值算例验证了所提设计方法的有效性。