A controller design based on a functional filter for descriptor systems: The time and frequency domain cases

In this paper, we investigate the time and frequency domain designs of a controller based on a functional filter for both continuous-time and discrete-time multivariable descriptor systems. The order of this controller is equal to the dimension of the state to be estimated, and the control gain is designed using H ∞ techniques. The time procedure is based on the unbiasedness of the estimation error using a Sylvester equation; then a new method for avoiding the derivative of the disturbance vector in the observation error dynamics is proposed. This problem is solved by means of linear matrix inequalities (LMIs). The frequency domain procedure design is derived from time domain results, where we propose some suitable matrix fraction descriptions (MFDs) and, most importantly, the factorization approach permits us to give a polynomial parameterization of the functional H ∞ filter-based controller.