Robust H_2/H_∞ control for a class of time-varying nonlinear stochastic systems with state- and control-dependent noises

摘要

This paper deals with the problem of robust control for a class of discrete time-varying nonlinear stochastic systems with state- and control-dependent noises (also called -dependent noises). In the addressed system, all system parameters are allowed to be time-varying, parameter uncertainties are supposed to be norm-bounded, and nonlinearities are assumed to satisfy the sector-bounded condition. A robust stochastic bounded real lemma is established for the uncontrolled system by means of the Riccati difference equation (RDE). Moreover, a necessary and sufficient condition is presented for the existence of finite-horizon robust control by virtue of the solvability of coupled RDEs, and an iterative algorithm is designed to solve these RDEs. Finally, a numerical example is utilised to illustrate the effectiveness of the derived results.