Robust Finite-Time H∞ Control of a Class of Disturbed Systems using Lmi-Based Approach

In this paper, the definition of robust finite-time H control is presented for a class of disturbed systems. Time-varying norm-bounded exogenous disturbance is considered in the system. A state feedback controller is designed, via a Linear Matrix Inequalities (LMIs) approach, which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. The main result, derived by Lyapunov functions, is a sufficient condition for FTB of disturbed systems and the sufficient condition can be reduced to a feasibility problem involving LMIs. Then a DC motor position control problem is simulated as a demonstration for this study. Simulation results are presented to show the effectiveness of the proposed method as a promising approach for controlling similar disturbed systems.