SUMMARYIn this paper, a solution to the approximate tracking problem of sampled-data systems with uncertain, time-varying sampling intervals and delays is presented. Such time-varying sampling intervals and delays can typically occur in the field of networked control systems. The uncertain, time-varying sampling and network delays cause inexact feedforward, which induces a perturbation on the tracking error dynamics, for which a model is presented in this paper. Sufficient conditions for the input-to-state stability (ISS) of the tracking error dynamics with respect to this perturbation are given. Hereto, two analysis approaches are developed: a discrete-time approach and an approach in terms of delay impulsive differential equations. These ISS results provide bounds on the steady-state tracking error as a function of the plant properties, the control design and the network properties. Moreover, it is shown that feedforward preview can significantly improve the tracking performance and an online extremum seeking (nonlinear programming) algorithm is proposed to online estimate the optimal preview time. The results are illustrated on a mechanical motion control example showing the effectiveness of the proposed strategy and providing insight into the differences and commonalities between the two analysis approaches.

. (2013). Stochastic hybrid systems with renewal transitions : moment analysis with application to networked control systems with delays. SIAM Journal on Control and Optimization, 51(2), 1481-1499. DOI: 10.1137/12087623X General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract. We consider stochastic hybrid systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an approach based on a set of Volterra equations to compute any statistical moment of the state of the SHS. Moreover, we provide a method to compute the Lyapunov exponents of a given degree, i.e., the exponential rate of decrease or increase at which statistical moments converge to zero or to infinity, respectively. We also discuss how, by computing the statistical moments, one can provide information about the probability distribution of the state of the SHS. The applicability of the results is illustrated in the analysis of a networked control problem with independently distributed intervals between data transmissions and delays.

SUMMARYWe address the problem of regulating a subset of outputs of a linear time‐invariant plant with multi‐rate measurements so as to achieve asymptotic tracking of an exogenous signal generated by the free motion of a linear time‐invariant system, denoted by exosystem. A solution to this problem is required to yield closed‐loop stability and should be such that output regulation is achieved even in the presence of small plant uncertainties and exogenous disturbances also generated by the exosystem. Contrarily to previous works, we propose a solution to the general case where the plant may have more measured outputs than inputs. We show that this solution allows us to solve simultaneous stabilization and output regulation problems that are not possible to solve through the previous works. Besides incorporating an internal model of the exosystem, the key feature of our proposed controller is that it includes a system that blocks signals generated by the exosystem arriving to the controller from the non‐regulated outputs. Copyright © 2012 John Wiley & Sons, Ltd.