Robust finite settling time stabilization of discrete time system with structured uncertainty

Abstract

The robust finite settling time (FST) stabilization problem is considered for an uncertain discrete time system. FST stability is a generalization of the dead-beat response [9], which requires that all the external signals as well as internal signals of a feedback system settle to new steady states after a finite time for any step inputs. The uncertain discrete time system under consideration is described by a causal real rational function which includes uncertain parameters, where the uncertain parameters are restricted to prescribed bounding intervals and enter affine linearly into the coefficients of the transfer functions.A necessary and sufficient condition for robust FST stability is presented in terms of a finite of transfer functions. The condition leads to a computationally verifiable necessary and sufficient condition for robust FST stabilizability and a systematic procedure for designing a robust FST feedback control system.