A discrete-time approach to the steady-state and stability analysis of distributed nonlinear autonomous circuits

We present a direct method for the steady-state and stability analysis of autonomous circuits with transmission lines and generic non- linear elements. With the discretization of the equations that describe the circuit in the time domain, we obtain a nonlinear algebraic formulation where the unknowns to determine are the samples of the variables directly in the steady state, along with the oscillation period, the main unknown in autonomous circuits.An efficient scheme to buildtheJacobian matrix with exact partial derivatives with respect to the oscillation period and with re- spect to the samples of the unknowns is described. Without any modifica- tion in the analysis method, the stability of the solution can be computed a posteriori constructing an implicit map, where the last sample is viewed as a function of the previous samples. The application of this technique to the time-delayed Chua's circuit (TDCC) allows us to investigate the stability of the periodic solutions and to locate the period-doubling bifurcations.Peer ReviewedPostprint (published version

A discrete-time approach to the steady-state and stability analysis of distributed nonlinear autonomous circuits

We present a direct method for the steady-state and stability analysis of autonomous circuits with transmission lines and generic nonlinear elements. With the discretization of the equations that describe the circuit in the time domain, we obtain a nonlinear algebraic formulation where the unknowns to determine are the samples of the variables directly in the steady state, along with the oscillation period, the main unknown in autonomous circuits. An efficient scheme to build the Jacobian matrix with exact partial derivatives with respect to the oscillation period and with respect to the samples of the unknowns is described. Without any modification in the analysis method, the stability of the solution can be computed a posteriori constructing an implicit map, where the last sample is viewed as a function of the previous samples. The application of this technique to the time-delayed Chua's circuit (TDCC) allows us to investigate the stability of the periodic solutions and to locate the period-doubling bifurcations.Peer ReviewedPostprint (published version

CHAOS SYNCHRONIZATION USING SUPER-TWISTING SLIDING MODE CONTROL APPLIED ON CHUA’S CIRCUIT

Chua’s circuit is the classic chaotic system and the most widely used in serval areas due to its potential for secure communication. However, developing an accurate chaos control strategy is one of the most challenging works for Chua’s circuit. This study proposes a new application of super twisting algorithm (STC) based on sliding mode control (SMC) to eliminate or synchronize the chaos behavior in the circuit. Therefore, the proposed control strategy is robust against uncertainty and effectively regulates the system with a good regulation tracking task. Using the Lyapunov stability, the property of asymptotical stability is verified. The whole of the system including the (control strategy, and Chua’s circuit) is implemented under a suitable test setup based on dSpace1104 to validate the effectiveness of our proposed control scheme. The experimental results show that the proposed control method can effectively eliminate or synchronize the chaos in the Chua's circuit

Advanced algorithms for the analysis of data sequences in Matlab

Cílem této práce je se seznámení s možnostmi programu Matlab z hlediska detailní analýzy deterministických dynamických systémů. Jedná se především o analýzu časové posloupnosti a o nalezení Lyapunových exponentů. Dalším cílem je navrhnout algoritmus umožňující specifikovat chování systému na základě znalosti příslušných diferenciálních rovnic. To znamená, nalezení chaotických systémů.This work aims to familiarize with the possibilities of Matlab in terms of detailed analysis of deterministic dynamical systems. This is essentially a analysis of time series and finding Lyapunov exponents. Another objective is to design an algorithm allowing to specify the system behavior based on knowledge of the relevant differential equations. That means finding chaotic systems.

Digital chaos analysis in optical logic structures

Digital chaotic behavior in an optically processing element is analyzed. It was obtained as the result of processing two fixed trains of bits. The process is performed with an optically programmable logic gate. Possible outputs, for some specific conditions of the circuit, are given. Digital chaotic behavior is obtained, by using a feedback configuration. Different ways to analyze a digital chaotic signal are presented