Using a new implicit discretization scheme, we study in this paper the existence and uniqueness of strong solutions for a class of Lur’e dynamical systems where the set-valued feedback depends on both the time and the state. This work is a generalization of Tanwani et al. (SIAM J. Control Opti. 56(2), 751–781, 2018) where the time-dependent set-valued feedback is considered to acquire weak solutions. Obviously, strong solutions and implicit discretization scheme are nice properties, especially for numerical simulations. Conditions guarantying the exponential attractivity of solutions are provided. The obtained results can be used to study the time-varying Lur’e systems with errors in data or under the state-dependent controls applied to the moving sets. Our work is new even the set-valued feedback depends only on the time.

中文翻译：

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具有状态依赖集值反馈的一类Lur'e动力系统

我们使用一种新的隐式离散化方案，研究了一类Lur'e动力系统强解的存在性和唯一性，其中，定值反馈取决于时间和状态。这项工作是Tanwani等人的概括。（SIAM J.控制的Opti。56（2），751–781，2018），其中时间相关的设定值反馈被认为可获得弱解。显然，强解和隐式离散化方案是很好的属性，尤其是对于数值模拟而言。提供了保证溶液指数吸引性的条件。所得结果可用于研究时变的Lur'e系统，该系统具有数据错误或在应用于移动集的状态相关控制下。即使设定值的反馈仅取决于时间，我们的工作也是新的。