Robust H2/H∞ control for a class of time-varying nonlinear stochastic systems with state- and control-dependent noises

Ming Gao, Zhengmao Zhu and Yichun Niu

International Journal of Systems Science, 2020, vol. 51, issue 7, 1218-1228

Abstract: This paper deals with the problem of robust $H_2/H_\infty $H2/H∞ control for a class of discrete time-varying nonlinear stochastic systems with state- and control-dependent noises (also called $(x,u) $(x,u)-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 $H_2/H_\infty $H2/H∞ 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.

Date: 2020
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DOI: 10.1080/00207721.2020.1755742

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