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— An intrinsic trajectory level approach without any recourse to an algebraic structure of a representation is utilized to develop a behavioural approach to robust stability. In particular it is shown how the controllable behaviour can be constructed at the trajectory level via Zorn's Lemma, and this is utilized to study the controllable-autonomous… (More)

We consider systems satisfying a matching condition which are functionally known up to weighted L 2 and L 1 measures of uncertainty. A modiied LQ measure of control and state transient performance is given, and the performance of a class of approximate model based adaptive controllers is studied. An upper performance bound is derived in terms of the… (More)

We consider the construction of adaptive controllers for minimum phase linear systems which achieve non-zero robustness margins in the sense of the gap metric. The gap perturbation margin may be more constrained for larger disturbances and for larger parametric uncertainties. Working in an L 2 setting, and within the framework of the nonlinear gap metric,… (More)

Graph topologies for nonlinear operators which admit coprime factorisations are defined w.r.t. a gain function notion of stability in a general normed signal space setting. Several metrics are also defined and their relationship to the graph topologies are examined. In particular, relationships between nonlinear generalisations of the gap and graph metrics,… (More)

We consider the adaptive tracking problem for a chain of integrators, where the uncertainty is static and functional. The uncertainty is speciied by L 2 =L 1 or weighted L 2 =L 1 norm bounds. We analyse a standard Lyapunov based adaptive design which utilizes a function approximator to induce a parametric uncertainty, on which the adaptive design is… (More)

The main result establishes that if a controller C (comprising of a linear feedback of the output and its derivatives) globally stabilizes a (nonlinear) plant P , then global stabilization of P can also be achieved by an output feedback controller C[h] where the output derivatives in C are replaced by an Euler approximation with sufficiently small delay h >… (More)

For any m-input, m-output, finite-dimensional, linear, minimum-phase plant P with first Markov parameter having spectrum in the open right-half complex plane, it is well known that the adaptive output feedback control C, given by u = −ky, ˙ k = y 2 , yields a closed-loop system [P, C] for which the state converges to zero, the signal k converges to a finite… (More)

This paper is concerned with the gap metric approach to controller discretisation problems for continuous-time nonlinear systems with disturbances in both input and output channels. The principal idea is to construct a discrete controller based on a given stabilizing continuous time controller via a fast sampling and hold procedure and to calculate the gap… (More)