In this paper, a polytopic control approach is applied to a PV-fed single-ended primary-inductance (SEPIC) dc-dc converter. In a clear-cut-contrast with conventional control techniques based on averaging procedures, the polytopic control approach is applied to the switched model of the system. In particular, the switching control signal is synthesized using a Lyapunov function which has polytopic level sets. The validity of the approach is illustrated and verified using numerical simulations showing that the controller can achieve good performance in terms of fast recovery due to input voltage variations.

In this paper, chaotic behavior of the Colpitts oscillator is studied and analyzed. The analyses consider the locally unstable behavior based on the linearization around the equilibrium and the globally bounded stability, which guarantees that the trajectories converge to an attractive and bounded set. The attractive set for the Colpitts oscillator is determined and characterized using Lyapunov analyses and an appropriate quadratic Lyapunov function. The theoretical results are accompanied by a representative simulation.

In this paper some local stability results for an autonomous Long Short-Term Memory neural network model with respect to the origin are provided. In particular, it is shown through linearization that the local asymptotic stability conditions with respect to the origin only depend on one of the weight matrices. Simulations indicate that these local stability conditions greatly influence the behavior of the autonomous four-dimensional neural network in the region where each variable's values vary between minus one and one. Finally, some sufficient stability conditions for the nonlinear model are formulated as a convex program involving linear matrix inequalities.

In this brief, the Ćuk dc/dc converter is controlled by a switching sequence based on the values of a polytopic Lyapunov function. In particular, the switching control signal is computed using a Lyapunov function which has polytopic level sets and it is not everywhere differentiable. The problem of not everywhere differentiability is handled using the Filippov's approach for discontinuous differential equations. The main advantage of the presented control design approach is that it provides exact computation of the state variables' ripple values which could not be obtained with previously used quadratic Lyapunov functions. The implementation particularities of the approach are illustrated and verified using a number of simulations.

This paper presents an approach to construct nonlinear control for switching DC-DC converters. What is presented are commonly used control methods and they are compared with nonlinear methods: sliding-mode control, hysteresis control and control using polytopic Lyapunov functions. In addition, an experimental realization of the sliding-mode controlled Buck converter is described in detail.

Design details and analysis of the properties of a hysteresis switching controller for the Ćuk converter are provided in this paper. The design is based on a switching control law which minimizes a common Lyapunov function derivative for the converter's continuous modes of operation. These continuous modes of operation are both marginally stable which causes some particularities in the design procedure. The design also meets the specifications in terms of the converter's duty ratio and the frequency limitations. The proposed hysteresis controller performance is analyzed with respect to the operating modes of the converter and illustrated with a number of representative and relevant simulations.