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

Prescribed Finite Time Stabilization of Linear Systems With State Constraints

“…The continuity of the switching function of ( 7) is guaranteed and it owns the ability to adjust the transient response performance. Lemma 3: For the coordinate transformation (8)(9)(10)(11), the inverse coordinate transformation s = P −1 w can be described as follows,…”

“…Remark 6: According to the block decomposition technique in Lemma 1 and Lemma 2, the original system (1) is transformed into the system (6), which owns the structure of different dimensions of subsystems. The coordinate transformation proposed in (8)(9)(10)(11) is utilized to obtain the transformed system ( 12) from (6). With the transformed system (12), if the state w i , i = 1, • • • , k − 1 is bounded, then the state w i−1 can be bounded in prescribed time T .…”