On the finite-time stability and stabilisation of LTI systems via an S-variable approach

Abstract

This paper deals with the finite-time boundedness (FTB) of linear time-invariant systems that are affected by a disturbance generated by an exosystem. By using a time-invariant quadratic Lyapunov function, Finsler's lemma and a dual system approach, new sufficient linear matrix inequalities (LMIs) conditions are given for analysis and synthesis for FTB. These results are extended: first, to finite-time stability (FTS) of linear time-invariant systems, second, to their input–output FTS associated, or not, to FTB. All the conditions are given in terms of LMIs, which make them easily tractable. Finally, the computational efficiency and the conservatism reduction of our approach are illustrated through an illustrative example.

Keywords:

• LTI systems
• linear matrix inequality (LMI)
• finite-time stability
• finite-time boundedness
• input–output finite-time stability
• state-feedback control

Disclosure statement

No potential conflict of interest was reported by the author(s).