Adaptive H∞H∞ control in finite frequency domain for uncertain linear systems

This paper is concerned with the problem of adaptive H∞H∞ controller design in finite frequency domains for uncertain linear systems. The uncertainties are assumed to be time-invariant, unknown, but bounded, which appear affinely in the matrices of system models. An adaptive mechanism is introduced to construct a novel finite frequency H∞H∞ controller with time-varying gains. By using Lyapunov theory and Parseval’s Theorem, the controller design conditions are given in terms of a set of linear matrix inequalities (LMIs). It is shown that the proposed finite frequency controller with time-varying gains can achieve better H∞H∞ performance than the traditional ones with fixed gains. Finally, a numerical example of the F-18 aircraft model is given to illustrate the presented theoretical results.