The study and the determination of polyhedral regions of local stability for linear systems subject to control saturation is addressed. The analysis of the nonlinear behavior of the closed-loop saturated system is made by dividing the state space in regions of saturation. Inside each of these regions, the system evolution can be represented by a linear system with an additive disturbance. From ...

The concepts of paracontracting, pseudocontracting and nonexpanding operators have been shown to be useful in proving convergence of asynchronous or parallel iteration algorithms. The purpose of this paper is to give characterizations of these operators when they are linear and finite-dimensional. First we show that pseudocontractivity of stochastic matrices with respect to ‖ · ‖∞ is equivalent...

In this work we are interested in the stability and L2-gain of hybrid systems with linear flow dynamics, periodic time-triggered jumps and nonlinear possibly set-valued jump maps. This class of hybrid systems includes various interesting applications such as periodic event-triggered control. In this paper we also show that sampled-data systems with arbitrarily switching controllers can be captu...

We present a trajectory tracking control design method for class of mechanical systems in the port-Hamiltonian framework. The proposed solution is based on virtual contractivity-based (v-CBC) method, which employs notions and contractivity. This approach leads to family asymptotic controllers that are not limited those preserve pH structure closed-loop system nor require an intermediate change ...

It is well known that a densely defined operator A on a Hilbert space is accretive if and only if A has a contractive H∞-calculus for any angle bigger than π 2 . A third equivalent condition is that ‖(A− w)(A + w)−1‖ ≤ 1 for all Rew ≥ 0. In the Banach space setting, accretivity does not imply the boundedness of the H∞-calculus any more. However, we show in this note that the last condition is s...

Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation.We consider generalizations of contractionwith respect to a norm that allow contraction to take place after small transients in time and/or amplitude. These generalized contractive systems (GCSs) are useful for seve...

One possible approach to exact real arithmetic is to use linear fractional transformations (LFT's) to represent real numbers and computations on real numbers. Recursive expressions built from LFT's are only convergent (i.e., denote a well-deened real number) if the involved LFT's are suuciently contractive. In this paper, we deene a notion of contrac-tivity for LFT's. It is used for convergence...