10 research outputs found
A Perron-Frobenius Theorem for Positive Quasipolynomial Matrices Associated with Homogeneous Difference Equations
We extend the classical Perron-Frobenius theorem for positive quasipolynomial matrices associated with homogeneous difference equations. Finally, the result obtained is applied to derive necessary and sufficient conditions for the stability of positive system
Observations on the Stability Properties of Cooperative Systems
We extend two fundamental properties of positive linear time-invariant (LTI) systems to homogeneous
cooperative systems. Specifically, we demonstrate that such systems are D-stable, meaning
that global asymptotic stability is preserved under diagonal scaling. We also show that a delayed
homogeneous cooperative system is globally asymptotically stable (GAS) for any non-negative delay if
and only if the system is GAS for zero delay
Vector Extensions of Halanay's Inequality
International audienceWe provide two extensions of Halanay's inequality, where the scalar function in the usual Halanay's inequality is replaced by a vector valued function, under a Metzler condition. We provide an easily checked necessary and sufficient condition for asymptotic convergence of the function to the zero vector in the time invariant case. For time-varying cases, we provide a sufficient condition for this convergence, which can be easily checked when the systems are periodic. We illustrate our results in cases that are beyond the scope of prior asymptotic stability results
Stability of positive linear Volterra integro-differential systems with delays
We study positive linear Volterra integro-differential systems with infinitely many delays. Positivity is characterized in terms of the system entries. A generalized version of the Perron-Frobenius Theorem is shown; this may be interesting in its own right but is exploited here for stability results: explicit spectral criteria for L1-stability and exponential asymptotic stability. Also the concept of stability radii, determining the maximal robustness with respect to additive perturbations to L1-stable system, is introduced and it is shown that the complex, real and positive stability radii coincide and can be computed by an explicit formula