Improved Discontinuous Lyapunov Functionals for Stability Analysis of Sampled-Data Systems

This paper is devoted to proposing improved discontinuous Lyapunov functionals for the stability analysis of sampled-data systems. Specifically, by relaxing the existing looped-functional, this paper makes the first attempt to integrate 1/t-t
_k
∫
_tk
^t
x(s)ds and 2/{({t-t
_k
}){2}}∫
_tk
^t
∫
_tk
^s
x(τ)dτs into the quadratic terms of the discontinuous Lyapunov functionals, which offer the possibility to obtain less conservative stability criteria formulated in terms of linear matrix inequalities (LMIs) than other previous studies. Finally, the effectiveness of the proposed Lyapunov functionals and corresponding approach are demonstrated by several numerical examples.