Finite time H_∞ filtering for uncertain discrete-time switching systems

The concept of finite-time stability (FTS) has gained much attention from researchers in recent years, after the emergent utilization of linear matrix inequalities (LMIs) in the field of control systems. In this paper, FTS and finite-time boundedness (FTB) analysis and synthesis procedure for a ‘finite-time H_∞ filter’ for discrete-time switching systems are presented. Assuming the external disturbance to be energy bounded, sufficient conditions for the designated H_∞ filter-based system to be finite-time stable are proposed. Considering dwell-time switching, average and minimum dwell time in terms of ‘finite-time’ system parameters has been formulated. Furthermore, these results are extended to uncertain switching system, by assuming the switching system subject to norm-bounded parameter uncertainties. The intended filter design steps have been demonstrated for both certain and uncertain system models. A cost function is introduced and then a parametric optimization algorithm is devised to calculate optimal filter parameters and present the derived results in LMI form. Numerical design examples are presented at the end to demonstrate the results.