Strict Lyapunov functions for time-varying systems with persistency of excitation

The class of discrete event dynamic systems involving only synchronization phenomena can be seen as linear time-invariant systems in a particular algebraic structure called ( min , +

For an undirected network of nonidentical interconnected Euler-Lagrange systems whose communication is affected by varying time-delays that may not be differentiable, we consider

In the present work it is shown that these conditions are similar, and that under such a relaxed excitation only non-uniform in time input-to-state stability and integral

A key feature of our analysis is that we do not require the Lyapunov functional to decay along trajectories when the delay is set to 0, which puts our strictification analysis

It is worth highlighting that the design of two bounds (i.e., the interval) for the solutions in fixed time can be done without requesting an appropriate knowledge of the interval

Usually, the existence of a common Lyapunov function implies stability for any switching signal, and we aim to establish stability results under restricted switching signals

In [14] this result has been extended to the class of time-varying systems, where constant and time-varying similarity transformations have been proposed to represent a

We present a reduction theorem for uniform asymptotic stability that completely addresses the local and global version of this problem, as well two reduction theorems for either