Abstract
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 $\frac {1}{t-t_{k}}\int _{t_{k}}^{t} x(s)ds$ and $\frac {2}{(t\!-\!t_{k})^{2}} \int _{t_{k}}^{t}\int _{t_{k}}^{s} x(\tau)d\tau ds$ 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.
Highlights
Over the past decades, sampled-data systems have attracted much attention from many researchers in the control community due to their compatibility with discrete-time control applications [11], [12], [20]
There have been some representative works related to sampled-data systems such as networked control systems [2], [21], event-based network consensus [17] and time-delay systems [19], [20]
In the Lyapunov-based approach, there have been a great deal of studies devoted to stability analysis of sampled-data linear systems such as time-dependent Lyapunov functional approach [4], [5], discontinuous Lyapunov functional technique [16], [18] and looped-functional-based method [23], [24]
Summary
Over the past decades, sampled-data systems have attracted much attention from many researchers in the control community due to their compatibility with discrete-time control applications [11], [12], [20]. There have been some representative works related to sampled-data systems such as networked control systems [2], [21], event-based network consensus [17] and time-delay systems [19], [20]. In the Lyapunov-based approach, there have been a great deal of studies devoted to stability analysis of sampled-data linear systems such as time-dependent Lyapunov functional approach [4], [5], discontinuous Lyapunov functional technique [16], [18] and looped-functional-based method [23], [24]. H. Kim: Improved Discontinuous Lyapunov Functionals for Stability Analysis at sampling instants to relax LMIs-based sufficient stability conditions. Motived by the above discussions, this short paper proposes improved discontinuous Lyapunov functionals for sampled data systems.
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