This paper examines the problem of designing an H∞ output feedback controller for a class of nonlinear singularly perturbed systems described by a TakagiSugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H∞ output feedback controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some pre...

We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers ẋ = y(−1+2αx+2βx), ẏ = x+α(y−x)+ 2βxy, α ∈ R, β < 0, when it is perturbed inside the classes of all continuous and discontinuous cubic polynomial differential systems. We obtain that the maximum number of limit cycles which can be obtained by the averaging...

This paper presents a new method for estimating the ultimate bound in perturbed systems. The methodology, exploiting the perturbation structure and the system geometry, gives an implicit expression of the ultimate bound which can be solved by fixed point iterations. Thus, it is simpler than the classic Lyapunov analysis and, in many cases, less conservative. Keywords— Nonlinear Systems, Perturb...

We study the bifurcation of limit cycles from periodic orbits of a four-dimensional systemwhen the perturbation is piecewise linear with two switching boundaries. Our main result shows that when the parameter is sufficiently small at most, six limit cycles can bifurcate from periodic orbits in a class of asymmetric piecewise linear perturbed systems, and, at most, three limit cycles can bifurca...

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of uncertain Markovian jump nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model with Markovian jumps. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear singularly perturbed systems to have an ...

We provide formulas to compute the coefficients entering the affine scaling needed to get a non-degenerate function for the asymptotic distribution of the maxima of some kind of observable computed along the orbit of a randomly perturbed dynamical system. This will give information on the local geometrical properties of the stationary measure. We will consider systems perturbed with additive no...

In this paper, we consider the weakened Hilbert’s 16th problem for symmetric planar perturbed polynomial Hamiltonian systems. In particular, a perturbed Hamiltonian polynomial vector field of degree 9 is studied, and an example of Z10-equivariant planar perturbed Hamiltonian systems is constructed. With maximal number of closed orbits, it gives rise to different configurations of limit cycles. ...

In this paper we discuss the computational power of Lipschitz dynamical systems which are robust to infinitesimal perturbations. Whereas the study in [1] was done only for not-so-natural systems from a classical mathematical point of view (discontinuous differential equation systems, discontinuous piecewise affine maps, or perturbed Turing machines), we prove that the results presented there ca...

this paper studies the perturbed klein-gordon equation by the aid of several methods of integrability. there are six forms of nonlinearity that are considered in this paper. the parameter domains are thus identified.

This paper is a survey of results presented in the recent book Gyllenberg and Silvestrov [GS08]. This book is devoted to studies of quasi-stationary phenomena for nonlinearly perturbed stochastic processes and systems. New methods of asymptotic analysis for nonlinearly perturbed stochastic processes based on asymptotic expansions for perturbed renewal equation and recurrence algorithms for cons...