Related papers: A tropical geometry approach to BIBO stability
Fractional difference equations provide a flexible mathematical framework for modeling complex systems with memory, hereditary, and non-local effects. In this work, we study the stability of higher-order two-term fractional linear…
Previous studies have inferred robust stability of reaction networks by utilizing linear programs or iterative algorithms. Such algorithms become tedious or computationally infeasible for large networks. In addition, they operate like…
This paper addresses the stabilization issue for fractional order switching systems. Common Lyapunov method is generalized for fractional order systems and frequency domain stability equivalent to this method is proposed to prove the…
In this paper we derive new criterion for uniform stability assessment of the linear periodic time-varying systems $\dot x=A(t)x,$ $A(t+T)=A(t).$ As a corollary, the lower and upper bounds for the Floquet characteristic exponents are…
In this paper we investigate the impact of delayed tax revenues on the fiscal policy out-comes. Choosing the delay as a bifurcation parameter we study the direction and the stability of the bifurcating periodic solutions. With respect to…
In this paper, the dynamics of a phytoplankton-zooplankton system with linear functional responses are examined. For the continuous-time model, the global asymptotic stability of the fixed points is demonstrated by constructing Lyapunov…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
We consider the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems. The problem can be solved, in principle, using real quantifier…
Using a Liao-type exponent, we study the stability of a time-varying nonlinear switching system.
This two-part paper series studies the performance of buffered Aloha networks with K-Exponential Backoff collision resolution algorithms. Part I focuses on stability and throughput analysis and Part II presents the delay analysis. In Part…
Many physical systems are inherently time-varying in nature. When these systems are linearized around a trajectory, generally, the resulting system is Linear Time-Varying (LTV). LTV systems describe an important class of linear systems and…
In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins production rate functions,…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
We consider classes of Boolean functions stable under compositions both from the right and from the left with clones. Motivated by the question how many properties of Boolean functions can be defined by means of linear equations, we focus…
Let K be a field equipped with a valuation. Tropical varieties over K can be defined with a theory of Gr{\"o}bner bases taking into account the valuation of K. Because of the use of the valuation, the theory of tropical Gr{\"o}bner bases…
This paper studies the stability of discrete-time polynomial dynamical systems on hypergraphs by utilizing the Perron-Frobenius theorem for nonnegative tensors with respect to the tensors Z-eigenvalues and Z-eigenvectors. Firstly, for a…
We present a numerical method to analyze the relative stability of closed-loop single-input-single-output (SISO) dead-time systems on a given left complex half-plane for all positive delays. The well-known boundary crossing method for the…
Failures in satellite components are costly and challenging to address, often requiring significant human and material resources. Embedding a hybrid AI-based system for fault detection directly in the satellite can greatly reduce this…
We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a…
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…