Renegotiation and Relative Performance Evaluation: Why an Informative Signal may be Useless

Although Holmström's informativeness criterion provides a theoretical foundation for the controllability principle and inter firm relative performance evaluation, empirical and field studies provide only weak evidence on such practices. This paper refines the traditional informativeness criterion by abandoning the conventional full-commitment assumption. With the possibility of renegotiation, a signal's usefulness in incentive contracting depends on its information quality, not simply on whether the signal is informative. This paper derives conditions for determining when a signal is useless and when it is useful. In particular, these conditions will be met when the signal's information quality is either sufficiently poor or sufficiently rich

A Joint Criterion for Reachability and Observability of Nonuniformly Sampled Discrete Systems

A joint characterization of reachability (controllability) and observability (constructibility) for linear SISO nonuniformly sampled discrete systems is presented. The work generalizes to the nonuniform sampling the criterion known for the uniform sampling. Emphasis is on the nonuniform sampling sequence, which is believed to be an additional element for analysis and handling of discrete systems.Comment: 8 pages, 1 figur

Beyond bilinear controllability : applications to quantum control

Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent works. Motivated by these applications, we give in this paper a criterion that applies to situations where the evolution operator is expressed as sum of possibly non-linear real functionals of the control that multiplies some time independent (coupling) operators

Controllability and controller-observer design for a class of linear time-varying systems

“The final publication is available at Springer via http://dx.doi.org/10.1007/s10852-012-9212-6"In this paper a class of linear time-varying control systems is considered. The time variation consists of a scalar time-varying coefficient multiplying the state matrix of an otherwise time-invariant system. Under very weak assumptions of this coefficient, we show that the controllability can be assessed by an algebraic rank condition, Kalman canonical decomposition is possible, and we give a method for designing a linear state-feedback controller and Luenberger observer

Non-linear eigenvalue problems arising from growth maximization of positive linear dynamical systems

We study a growth maximization problem for a continuous time positive linear system with switches. This is motivated by a problem of mathematical biology (modeling growth-fragmentation processes and the PMCA protocol). We show that the growth rate is determined by the non-linear eigenvalue of a max-plus analogue of the Ruelle-Perron-Frobenius operator, or equivalently, by the ergodic constant of a Hamilton-Jacobi (HJ) partial differential equation, the solutions or subsolutions of which yield Barabanov and extremal norms, respectively. We exploit contraction properties of order preserving flows, with respect to Hilbert's projective metric, to show that the non-linear eigenvector of the operator, or the "weak KAM" solution of the HJ equation, does exist. Low dimensional examples are presented, showing that the optimal control can lead to a limit cycle.Comment: 8 page