Finite‐time bounded stabilisation for linear systems with finite‐time H 2 ‐gain constraint

This study discusses the finite-time boundedness (FTB) of the state of linear systems with a finite-time H 2-gain performance constraint. With time-varying exogenous disturbances, the sufficient conditions for linear time-invariant and linear time-varying systems to satisfy both the FTB constraint and the finite-time H 2-gain performance constraint are developed. On the basis of the matrix inequality theory, a method for designing a controller by using state feedback is derived for each of the two classes of linear systems. These methods can effectively keep the state from reaching an unacceptable value and modulate the output performance within a specified finite-time interval. Two application examples of the terminal guidance scenario verify the effectiveness of the proposed methods.