in this paper, we introduce a new hyperchaotic complex t-system. this system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. we discuss the synchronization with certain and uncerta...

In this paper, we introduce Lyapunov measure to verify weak (a.e.) notions of stability for an invariant set of a nonlinear dynamical system. Using certain linear operators from Ergodic theory, we derive Lyapunov results to deduce a.e. stability. In order to highlight the linearity of our approach, we also provide explicit formulas for obtaining Lyapunov function and Lyapunov measure in terms o...

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic sy...

The Lyapunovmethod for stability analysis of an equilibrium state of a nonlinear dynamic system requires a Lyapunov function v(t, x) having the following properties: (1) v is a positive definite function, and (2) v̇ is at least a negative semi-definite function. Finding such a function is a challenging task. The first theorem presented in this paper simplifies the second property for a Lyapunov ...

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...