This paper proposes a novel approach based on Lyapunov function method to analyse the stability of photovoltaic (PV) systems. The Lyapunov function is formulated using the method of quadratic forms, i.e., Krasovskii’s method. The stability of the photovoltaic systems under different operating conditions is analysed based on the formulated Lyapunov function. A comparison of stability analysis us...

In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function) in the optimal stabilization problem of smooth finite-dimensional systems 3 Geometrical methods. Continuation In the given section the greater attention is given to invariant description of the potential function and its Lagrange...

In this paper, the common centralized DEA models are extended to the bi-level centralized resource allocation (CRA) models based on revenue efficiency. Based on the Karush–Kuhn–Tucker (KKT) conditions, the bi-level CRA model is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). A recurrent neural network is developed for solving this one-level mathematica...

A Lyapunov function for excitatory-inhibitory networks is constructed. The construction assumes symmetric interactions within excitatory and inhibitory populations of neurons, and antisymmetric interactions between populations. The Lyapunov function yields su cient conditions for the global asymptotic stability of xed points. If these conditions are violated, limit cycles may be stable. The rel...

This paper discusses the application of Lyapunov theory in chaotic systems to the dynamics of tracer gradients in two-dimensional flows. The Lyapunov theory indicates that more attention should be given to the Lyapunov vector orientation. Moreover, the properties of Lyapunov vectors and exponents are explained in light of recent results on tracer gradients dynamics. Differences between the diff...

This paper investigates 2D mixed continuous-discrete-time systems whose coefficients are polynomial functions of an uncertain vector constrained into a semialgebraic set. It is shown that a nonconservative linear matrix inequality (LMI) condition for ensuring robust stability can be obtained by introducing complex Lyapunov functions depending polynomially on the uncertain vector and a frequency...

For dynamical systems defined by vector fields over a compact invariant set, we introduce a new class of approximated first integrals based on finite-time averages and satisfying an explicit first order partial differential equation. Referring to the PDE framework, we detect their viscosity robustness with respect to stochastic perturbations of the vector field. We formulate this approximating ...

The paper considers parametric uncertain systems of the form ẋ t Mx t ,M ∈ M,M ⊂ Rn×n, where M is either a convex hull, or a positive cone of matrices, generated by the set of vertices V {M1,M2, . . . ,MK} ⊂ Rn×n. Denote by μ‖ ‖ the matrix measure corresponding to a vector norm ‖ ‖. When M is a convex hull, the condition μ‖ ‖ Mk ≤ r < 0, 1 ≤ k ≤ K, is necessary and sufficient for the existence ...

In this paper, the decomposition-aggregation method is used to carry out connective stability criteria for general linear composite system via aggregation. The large scale system is decomposed into a number of subsystems. By associating directed graphs with dynamic systems in an essential way, we define the relation between system structure and stability in the sense of Lyapunov. The stability ...