H∞ Control of a Building Structure with Time-Varying Delay

In this paper, a H-infinity controller for a building structure with time-varying delay is studied. A matrix inequality used for stability analysis is proposed, an H-infinity controller is designed based on the matrix inequality and by using the parameter-adjusting method. Three control cases are discussed detailly by transforming the problem into parameters optimization: (i) allowable time delay with known controller; (ii) controller design with known maximum time delay; (iii) the biggest allowable time delay to maintain system stability with unknown controller. Numerical simulations are also given to demonstrate the validity and feasibility of the proposed methods in this paper.