Nonlinear time series analysis
Nonlinear time series analysis
Control of Chaos: Methods and Applications. I. Methods
Automation and Remote Control
Contribution to analysis of conservativity, dissipativity and system stability
ISTASC'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Systems Theory and Scientific Computation - Volume 7
Structual approach to instability and chaos in non-linear causal systems
ISTASC'07 Proceedings of the 7th Conference on 7th WSEAS International Conference on Systems Theory and Scientific Computation - Volume 7
ICC'05 Proceedings of the 9th International Conference on Circuits
Signal energy-metric approach to stability analysis of linear and non-linear causal systems
AEE'05 Proceedings of the 4th WSEAS international conference on Applications of electrical engineering
On synthesis of asymptotic filter banks based on a generalization of the Tellegen's principle
AEE'05 Proceedings of the 4th WSEAS international conference on Applications of electrical engineering
On state space energy controlled systems with quantum chaotic-like behavior
CSS'11 Proceedings of the 5th WSEAS international conference on Circuits, systems and signals
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Almost in any field of science and technology some sort of stability problem can appear. Instability and chaos are certainly the most important phenomena which should be treated before any other aspect of reality will be attacked. Hence it is not very surprising that a broad variety of approaches to the problem of stability, instability and analysis of chaotic phenomena exists. Many of the most popular techniques in the field of stability and chaos are in a certain sense related to the work of A.M.Lyapunov and can be seen as energy oriented. Tellegen's theorem is one of the well known forms of energy conservation statement in the field of electrical engineering. The most important feature of Tellegen's approach is the fact that the energy conservation principle holds without any regard to physical nature of constituent network elements. This is the key idea of the proposed approach to problems of dissipativity and chaos. The first one arises if an energy function E[x(t)] of a given system is known in a mathematical form. In such situations the time evolution of internal energy along any system motion can be described, and an energy monotonicity test can be used. In the proposed paper a physically motivated signal-system-theoretic approach to chaotic phenomena, based on a generalisation of the well known Tellegen's principle of electrical circuits will be presented and used as a fundamental tool to solve problems of chaos detection, analysis, synthesis and control from a unique physically plausible point of view. Two fundamental concepts are of crucial importance in the proposed approach. The first one is the concept of strongly non-linear power-informational interactions, and the second one is the notion of state space energy vector, inducing the system state-space topology. All computations, including numerical solutions of differential equations, were done using MATLAB.