We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov–Metzler inequalities and on a matrix S-lemma, we derive data-dependent bilinear programs, whose solution directly returns a provably stabilizing controller and ensures H2 or H∞ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for an unknown perturbed linear system. We validate our theoretical findings numerically, demonstrating the favorable trade-off between conservatism and tractability achieved by the proposed relaxations.

中文翻译：

---

数据驱动的开关和约束线性系统的稳定性


考虑到过去的噪声输入状态轨迹测量，我们考虑了未知开关线性系统的开关信号和连续输入的状态反馈控制律的设计。基于 Lyapunov-Metzler 不等式和矩阵 S 引理，我们推导出数据依赖的双线性程序，其解直接返回一个可证明的稳定控制器并确保 H2 或 H∞ 性能。我们进一步提出了大大降低计算成本的松弛，仍然不需要任何开关模式的稳定性。最后，我们展示了我们在未知扰动线性系统的约束稳定问题上的方法的灵活性。我们从数字上验证了我们的理论发现，证明了所提出的放松措施在保守性和可追踪性之间实现了有利的权衡。