Stochastic control of unified decentralized singularly perturbed systems

Abstract

The design of a stochastic optimal controller using state feedback and output feedback is developed for unified, decentralized, singularly perturbed systems with Gaussian noise. To filter out the external noises contained in the system signals, a unified optimal observer (Kalman filter) is used for the decentralized, singularly perturbed system with a reduced-order model. The reduced-order stabilizing observer is also derived by the unified Riccati equation approach. Rationalization of the decentralized, singularly perturbed system with time delays is presented in the frequency domain by using the delta operator approach. It is shown that the discrete-time system is realized into the discrete-time state-space model. The stability robustness of a unified decentralized singularly perturbed stochastic system is investigated by exploring stability bounds under system uncertainties. A new unified stochastic bound is derived for both "unstructured" and "structured" time-varying independent perturbations.