Abstract
This article addresses the robust fixed-time stabilization control problem for generic linear systems with both matched and mismatched disturbances. A new observer-based fixed-time control technique is proposed to solve this robust stabilization problem, provided that the system matrix pair <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(A,B)$ </tex-math></inline-formula> is controllable. The ultimate boundedness of the closed-loop system in the presence of mismatched disturbances is proven. An upper bound of the convergence time is provided, which is irrelevant to initial conditions. Finally, a simulation example is presented to show the efficiency of the proposed control design method.
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