The formulation of the process of analog system design has been done on the basis of the control theory application as the problem of a special functional minimization. This approach generalizes the design process and produces the different design trajectories inside the same optimization procedure. Numerical examples show that the potential computer time gain of the optimal design strategy wit...

A relaxation of Lyapunov’s direct method has been proposed recently that allows for an algorithmic construction of Lyapunov functions to prove stability of equilibria in nonlinear systems, but the search is restricted to systems with polynomial vector fields. In this paper, the above technique is extended to include systems with equality, inequality, and integral constraints. This allows certai...

Abstract— This paper extends the quotient method proposed in [1] and applies it to stabilize a “ball-on-a-wheel” system. The quotient method requires a diffeomorphism to obtain the normal form of the input vector field and uses canonical projection to obtain the quotient. However, the whole process can be done without computing the normal form, which requires defining a quotient generating func...

the present article deals with the inter specific competition and intra-specific competition among predator populations of a prey-dependent three component food chain model consisting of two competitive predator sharing one prey species as their food. the behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. boundedness and dissipativeness of the system are e...

Abstract: In this paper we investigate some stochastic models for tumor-immune systems. To describe these models, we used a Wiener process, as the noise has a stabilization effect. Their dynamics are studied in terms of stochastic stability in the equilibrium points, by constructing the Lyapunov exponent, depending on the parameters that describe the model. Stochastic stability was also proved ...

Lyapunov functions are a fundamental tool to investigate stability properties of equilibrium points of linear and nonlinear systems. The existence of Lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse Lyapunov theorems. Nevertheless the actual computation (of the analytic expression) of the function may be difficult. Herein we propose an approach to avoid ...

We introduce the concept of sos-convex Lyapunov functions for stability analysis of discrete time switched systems. These are polynomial Lyapunov functions that have an algebraic certificate of convexity, and can be efficiently found by semidefinite programming. We show that sos-convex Lyapunov functions are universal (i.e., necessary and sufficient) for stability analysis of switched linear sy...

In this paper, the impulsive fuzzy recurrent neural network with both time-varying delays and distributed delays is considered. Applying the idea of vector Lyapunov function, M-matrix theory and analytic methods, several sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the addressed neural network. Moreover, the est...

We present a qualitative analysis of the Lotka-Volterra differential equation within rectangles that are transverse with respect to the flow. In similar way to existing works on affine systems (and positively invariant rectangles), we consider here nonlinear Lotka-Volterra n-dimensional equation, in rectangles with any kind of tranverse patterns. We give necessary and sufficient conditions for ...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...