\(H_\infty\)-control for linear time-delay systems with Markovian jumping parameters
The goal of the authors is to extend some results concerning an \(H_\infty\)-control problem and its robustness obtained previously for the class of linear time-delay systems to the special linear time-delay systems with Markovian jumping parameters (LTDSMJP). The class of uncertain LTDSMJP with external disturbance is considered. The dynamics of the systems includes state vector, control input, disturbance input, controlled output, the function with a time-delay and norm-bounded uncertainties of two types: nonlinear bounded and norm-bounded uncertainties. Based on a Lyapunov functional approach, a sufficient condition that assures the robust stochastic stabilizability and preserves the \(H_\infty\)-disturbance attenuation of level \(\gamma\) for LTDSMJP is established. The results are based on the solution to a set of coupled algebraic Riccati equations via a combination of the algorithms of Abou-Kandil and Petersen. An illustrative numerical example is presented.
scientific article; zbMATH DE number 1506898