Abstract We introduce an event-triggered algorithm for the stabilization of switched linear systems. We define a pseudo-Lyapunov function common to all the subsystems. The pseudo-Lyapunov function is compared, at every time instant, to an exponentially decreasing upper threshold. An event is generated when the two functions intersect, or when a new subsystem becomes active. The existence of a Lyapunov function common to all the subsystems is a key requirement of this method. Nevertheless, imposing this condition does not add to the complexity of the problem. Indeed, we formulate the problem in terms of Linear Matrix Inequalities, as a generalized eigenvalue problem. This formulation allows to simultaneously check for the existence of a common Lyapunov function and to obtain the optimal parameters to define the upper threshold. We prove the stability of the system under the event-triggered control and we show that successive events are separated by a minimum interval of time.

中文翻译：

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用于切换线性系统的事件触发稳定控制器

摘要 我们介绍了一种用于稳定切换线性系统的事件触发算法。我们定义了所有子系统通用的伪李雅普诺夫函数。伪李雅普诺夫函数在每个时刻都与指数递减的上限阈值进行比较。当两个函数相交时，或者当一个新的子系统被激活时，就会生成一个事件。所有子系统共有的李雅普诺夫函数的存在是该方法的关键要求。然而，强加这个条件并不会增加问题的复杂性。实际上，我们根据线性矩阵不等式将问题表述为广义特征值问题。该公式允许同时检查公共李雅普诺夫函数的存在并获得定义上限阈值的最佳参数。