This paper considers uncertain systems from a behavioural point of view defined via quadratic differential forms. This uncertainty definition is closely related to the integral quadratic constraint uncertainty description commonly found in robust control theory. The paper presents a frequency domain condition for the set of behaviours of a given uncertain system to contain the set of behaviours...

Based on the concept of an interval-valued function which is motivated by the goal to represent an uncertain function, we define the Choquet integral with respect to a fuzzy measure of intervalvalued functions. We also discuss convergence in the C mean and convergence in a fuzzy measure of sequences of measurable interval-valued functions. In particular, we investigate the convergence theorem f...

The concept of an interval-valued capacity is motivated by the goal to generalize a capacity, and it can be used for representing an uncertain capacity. In this paper, we define the discrete intervalvalued capacities, a measure of the entropy of a discrete interval-valued capacity, and, Choquet integral with respect to a discrete interval-valued capacity. In particular, we discuss the Choquet i...

It is well-known from linear systems theory that an integral control law is needed for asymptotic set-point regulation under parameter perturbations. This paper presents a similar result for a class of nonlinear systems in the presence of an unknown equilibrium due to uncertain nonlinearities and dynamic uncertainties. Both partial-state and output feedback cases are considered. A procedure for...

A boundary integral operator method for stochastic ray tracing in billiards was recently proposed in [1]. In particular, a phase-space boundary integral model for propagating uncertain ray or particle flows was described and shown to interpolate between deterministic and random models of the flow propagation. In this work we describe discretisation schemes for this class of boundary integral op...