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We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…
Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the…
In this paper we consider distributed adaptive stabilization for uncertain multivariable linear systems with a time-varying diagonal matrix gain. We show that uncertain multivariable linear systems are stabilizable by diagonal matrix high…
Experimental manipulations perturb the neuronal activity. This phenomenon is manifested in the fMRI response. Dynamic causal model and its variants can model these neuronal responses along with the BOLD responses [1, 2, 3, 4, 5] .…
In this paper, a polynomial chaos based framework for designing controllers for discrete time linear systems with probabilistic parameters is presented. Conditions for exponential-mean-square stability for such systems are derived and…
In this paper, we address the problem of computing the maximal admissible robust positive invariant (MARPI) set for discrete-time linear time-varying systems with parametric uncertainties and additive disturbances. The system state and…
In this paper, we study the internal stabilizability and internal stabilization problems for multidimensional (nD) systems. Within the fractional representation approach, a multidimen-sional system can be studied by means of matrices with…
We obtain the most general matrix criterion for stability and instability of multi-component solitary waves considering a system of $N$ incoherently coupled nonlinear Schrodinger equations. Soliton stability is studied as a constrained…
This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting…
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
This paper proposes a decentralized method for regional pole placement, or $\mathcal{D}$-stability, in linearized networked systems. Existing LMI-based methods are hindered by confidentiality concerns regarding proprietary subsystem models…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov-Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen's and Wirtinger's…
This paper considers $L_2$ and BIBO stability and stabilization issues for systems with time-varying delays which can be of retarded or neutral type. An important role is played by a nominal system with fixed delays which are close to the…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
In this paper, we obtain sufficient conditions for the permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed…
The robust instability of an unstable plant subject to stable perturbations is of significant importance and arises in the study of sustained oscillatory phenomena in nonlinear systems. This paper analyzes the robust instability of linear…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…