Dynamic control for non-linear systems with delay
The paper is devoted to nonlinear systems with time-varying delay of the form \[ \dot x = A(\cdot)x + \sum_{i = 1}^l A_i (\cdot)x(t - \tau_i (t)) + b(\cdot)u, \] where \(A(\cdot) \in \mathbb{R}^{n \times n}\), \(A_i(\cdot) \in \mathbb{R}^{n \times n}\), \(b(\cdot) \in \mathbb{R}^n\), whose entries are arbitrary uniformly bounded functionals. For this class of systems, the authors derive sufficient conditions of existence and describe a method for reconstruction of a continuous or pulse dynamic control that makes the system globally asymptotically stable. Namely, a special type of the Lyapunov-Krasovskii functional is used to synthesize dynamic control described by the equation \[ \dot u = \rho (\cdot)u + (m(\cdot),x), \] where \(\rho (\cdot) \in \mathbb{R}^1\), \(m(\cdot) \in \mathbb{R}^n\).
scientific article; zbMATH DE number 6109188