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A model is proposed for a class of asynchronous sample-and-hold operators that is relevant to the analysis of embedded and networked systems. The model is parametrized by characteristics of the corresponding time-varying input–output delay. Uncertainty in the relationship between the timing of zero-order-hold update events at the output and the possibly aperiodic sampling events at the input means that the delay does not always reset to a fixed value. This is distinct from the well-studied synchronous case in which the delay intermittently resets to zero at output update times. The main result provides a family of integral quadratic constraints that covers the proposed model. To demonstrate an application of this result, stability and performance certificates are devised for an asynchronous sampled-data implementation of the feedback loop around given linear time-invariant continuous-time open-loop dynamics. Numerical examples are also presented. [ABSTRACT FROM AUTHOR]

This technical note elaborates on the flexibility of an approach that combines \nu-gap metric and integral quadratic constraint (IQC) based analysis in the study of uncertain feedback interconnections of distributed-parameter transfer functions. It is established that a standard \nu-gap ball robust stability result can be recovered within the blended IQC/\nu-gap framework, which only requires the existence of \nu-gap continuous paths within the uncertainty set of interest. This is achieved, in part, by showing that sufficiently small \nu-gap balls are pathwise connected in the graph topology. A linear fractional characterisation of the \nu-gap is a key ingredient. This characterisation is underpinned by a certain J-spectral factorisation, also shown to exist herein. [ABSTRACT FROM AUTHOR]

A framework is established for directly accommodating feedback interconnections of unstable distributed-parameter transfer functions in robust stability analysis via integral quadratic constraints (IQCs). This involves transfer function homotopies that are continuous in a \nu-gap metric sense. As such, the development includes the extension of \nu-gap metric concepts to an irrational setting and the study of uncertainty-set connectedness in these terms. The main IQC based robust stability result is established for constantly-proper transfer functions in the Callier-Desoer algebra; i.e. finitely many unstable poles and a constant limit at infinity. Problems of structured robust stability analysis and robust performance analysis are considered to illustrate use of the main result. Several numerical examples are also presented. These include stability analysis of an autonomous system with uncertain time-delay and a closed-loop control system, accounting for both the gain and phase characteristics of the distributed-parameter uncertainty associated with the nominal rational plant model used for controller synthesis. [ABSTRACT FROM AUTHOR]