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On delay-dependent robust stability under model transformation of some neutral systems

Salvador A. Rodríguez, Luc Dugard, Jean-Michel Dion, Jesús de León (2009)

Kybernetika

This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust stability...

On generalized inverses of singular matrix pencils

Klaus Röbenack, Kurt Reinschke (2011)

International Journal of Applied Mathematics and Computer Science

Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate singular matrix pencils. The relations between the Kronecker structure of a singular matrix pencil and the...

On Lagrangian systems with some coordinates as controls

Franco Rampazzo (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let Σ be a constrained mechanical system locally referred to state coordinates ( q 1 , , q N , γ 1 , , γ M ) . Let ( γ ~ 1 γ ~ M ) ( ) be an assigned trajectory for the coordinates γ α and let u ( ) be a scalar function of the time, to be thought as a control. In [4] one considers the control system Σ γ ^ , which is parametrized by the coordinates ( q 1 , , q N ) and is obtained from Σ by adding the time-dependent, holonomic constraints γ α = γ ^ α ( t ) := γ ~ α ( u ( t ) ) . More generally, one can consider a vector-valued control u ( ) = ( u 1 , , u M ) ( ) which is directly identified with γ ^ ( ) = ( γ ^ 1 , , γ ^ M ) ( ) . If one denotes the momenta conjugate...

On the dynamics of a vaccination model with multiple transmission ways

Shu Liao, Weiming Yang (2013)

International Journal of Applied Mathematics and Computer Science

In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number below unity....

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