标题： 具有长时间输入延迟的线性切换系统的平均预测器反馈镇定 显示英文标题

标题： Stabilization of Linear Switched Systems with Long Input Delay via Average or Averaging Predictor Feedbacks

摘要： 我们为具有时变切换的线性切换系统开发了延迟补偿反馈律。由于构建精确预测器-反馈律所需的未来切换信号值可能在当前时间不可用，因此关键设计挑战是如何构造适当的预测状态。我们通过构建两种替代的基于平均预测器的反馈律解决了这个挑战。第一种被视为针对特定平均系统的预测器-反馈律，经过适当修改以在整个依赖于切换信号最小驻留时间（当其可用时）的时间范围内提供精确的状态预测。第二种本质上是对每个固定模式预测器-反馈律对应的预测器反馈平均值的修改。我们证明，在引入的控制律下，闭环系统在系统矩阵之间以及（名义稳定化）控制器增益之间的差异足够小时是（一致地）指数稳定的，这种差异的大小与延迟长度成反比。由于没有对延迟施加限制，这种限制是所考虑问题固有的（其中未来的切换信号值不可用），因此无法消除。稳定性证明依赖于通过反向步进构造的多个李雅普诺夫泛函和解估计的推导，用于量化平均预测器状态和精确预测器状态之间的差异。我们展示了具有一致性的数值模拟结果，这些结果说明了使用基于平均预测器的律的必要性，并且展示了当正确利用最小驻留时间来提高状态预测精度时性能的改善。 显示英文摘要

摘要： We develop delay-compensating feedback laws for linear switched systems with time-dependent switching. Because the future values of the switching signal, which are needed for constructing an exact predictor-feedback law, may be unavailable at current time, the key design challenge is how to construct a proper predictor state. We resolve this challenge constructing two alternative, average predictor-based feedback laws. The first is viewed as a predictor-feedback law for a particular average system, properly modified to provide exact state predictions over a horizon that depends on a minimum dwell time of the switching signal (when it is available). The second is, essentially, a modification of an average of predictor feedbacks, each one corresponding to the fixed-mode predictor-feedback law. We establish that under the control laws introduced, the closed-loop systems are (uniformly) exponentially stable, provided that the differences among system's matrices and among (nominal stabilizing) controller's gains are sufficiently small, with a size that is inversely proportional to the delay length. Since no restriction is imposed on the delay, such a limitation is inherent to the problem considered (in which the future switching signal values are unavailable), and thus, it cannot be removed. The stability proof relies on multiple Lyapunov functionals constructed via backstepping and derivation of solutions' estimates for quantifying the difference between average and exact predictor states. We present consistent numerical simulation results, which illustrate the necessity of employing the average predictor-based laws and demonstrate the performance improvement when the knowledge of a minimum dwell time is properly utilized for improving state prediction accuracy.