Input–output stabilization-based finite-time robust control of disturbed systems using linear matrix inequality approach

In this paper, finite-time robust control problems are considered for a class of uncertain systems subject to exogenous disturbances, and an input–output finite-time stabilization (IO-FTS) method is presented with finite-time boundedness (FTB) constraints. For an uncertain system, a state feedback controller is designed, via linear matrix inequalities (LMIs), to ensure the IO-FTS and FTB of the closed-loop system. By using Lyapunov stability theory, sufficient conditions for IO-FTS and FTB are given. These conditions are expressed as a feasibility problem of a set of LMIs. The direct current motor control problem and roll autopilot design of a skid-to-turn missile are considered for a case study. Simulation results are presented to show the effectiveness of the proposed method as a promising approach to controlling similar uncertain systems.