Singular nonlinear systems has been of interest to some investigators [4, 12], however no closed-form solution was given in [4, 12]. In some analysis of neural networks, both singular systems [8] and bilinear systems [16] have been used. For singular bilinear systems, Lewis et al. [11] applied the Walsh function (WF) approach for time-invariant singular bilinear systems and Hsiao and Wang [9] u...

This note concerns the delay-dependent robust stability analysis for uncertain singular time-delay systems. The parameter uncertainty is assumed to be norm-bounded and possibly time-varying, while the time delay considered here is assumed to be constant but unknown. By using a new Lyapunov-krasovskii functional which splits the whole delay interval into two subintervals and defines a different ...

In order to ensure stability of the system, transmission and distribution studies need to be performed. These simulation studies can be time consuming due to high complexity of the system. This paper investigates model reduction on a power system with photovoltaic generation. This is done by decreasing the complexity of the detailed model, which leads to a smaller simulation time, but still mai...

There exists a property “structural stability” for “4-dimensional canards” which is singular-limit solution in slow-fast system with bifurcation parameter. It means that the includes possibility to have some critical values on Corresponding these values, pseudo-singular point, singular point time-scaled-reduced should be changed another one. Then, canards may fly if possible. Can fly? The struc...

We present a general method for solving the non–linear differential equation of monotonically increasing steady–state radiation driven winds. We graphically identify all the singular points before transforming the momentum equation to a system of differential equations with all the gradients explicitly give. This permits a topological classification of all singular points and to calculate the m...

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

The "tea-cup" attractor of a classical prey-predator-superpredator food chain model is studied analytically. Under the assumption that each species has its own time scale, ranging from fast for the prey to intermediate for the predator and to slow for the superpredator, the model is transformed into a singular perturbed system. It is demonstrated that the singular limit of the attractor contain...

This note is concerned with the observer design problem for a class of linear delay systems of the neutral-type. The problem addressed is that of designing a full-order observer that guarantees the exponential stability of the error dynamic system. An effective algebraic matrix equation approach is developed to solve this problem. In particular, both observer analysis and design problems are in...