In this paper, a chattering-free sliding-mode control is mainly proposed in a second-order discrete-time system. For achieving this purpose, firstly, a suitable control law would be derived by using the discrete-time Lyapunov stability theory and the sliding-mode concept. Then the input constraint is taken into account as a saturation function in the proposed control law. In order to guarantee ...

We propose an algorithm for the approximation of stable and unstable fibers that applies to autonomous as well as to nonautonomous ODEs. The algorithm is based on computing the zero-contour of a specific operator; an idea that was introduced in [Hüls, 2014] for discrete time systems. We present precise error estimates for the resulting contour algorithm and demonstrate its efficiency by computi...

In this paper, the problem of second–order consensus in multi–agent systems with sampled position data is handled. Due to the discrete nature of the information transmission among agents, there is an increasing interest in such kind of systems. By thinking of collecting sampled position data in a certain time interval, that is more general than considering just the sampling period as in many pa...

Coexisting periodic solutions of a dynamical system describing nonlinear optical processes of the second-order are studied. The analytical results concern both the simplified autonomous model and the extended nonautonomous model, including the pump and damping mechanism. The nonlinearity in the coexisting solutions of the autonomous system is in concealed frequencies depending on the initial co...