Robust observer-based finite-time H∞ control for one-sided Lipschitz singular systems with uncertainties

This study deals with the problem of observer-based finite-time H-infinity control for a class of one-sided Lipschitz (OSL) singular systems with uncertainties. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in both the state and output matrices but also in the non-linear function. With the help of some special derivations and transformation, the sufficient conditions ensuring robust finite-time boundedness of the closed-loop system and satisfying the H-infinity performance index are given for OSL singular systems in terms of linear matrix inequalities (LMIs). Based on these, the observer and controller dynamics can be simultaneously involved in the design at one step. Two convex optimisation problems subject to LMIs are formulated to optimise the desired performance indices of interest to us. Finally, two examples are given to demonstrate the effectiveness of the proposed methods.