Central suboptimal mean-square H ∞ controller design for linear stochastic time-varying systems

Abstract

This article designs the central finite-dimensional H ∞ controller for linear stochastic time-varying systems with integral-quadratically bounded deterministic disturbances, that is suboptimal for a given threshold γ with respect to a modified Bolza–Meyer quadratic criterion including the attenuation control term with the opposite sign. In contrast to the previously obtained results, this article reduces the original H ∞ controller problem to the corresponding optimal H 2 controller problem, using the technique proposed in Doyle et al. (Doyle, J.C., Glover, K., Khargonekar, P.P., and Francis, B.A. (1989), ‘State-space Solutions to Standard H 2 and H ∞ Control Problems’, IEEE Transactions on Automatic Control, 34, 831–847). Numerical simulations are conducted to verify the performance of the designed controller for a linear stochastic system against the central suboptimal H ∞ controller available for the corresponding deterministic system.