On a Class of Lur’e Dynamical Systems with State-Dependent Set-Valued Feedback

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.