CLF based designs with robustness to dynamic input uncertainties

The problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation. Stabilizing control laws may not be robust to this type of uncertainty, especially if cancellation of nonlinearities is used in the design. By exploiting a connection between robustness and optimality, "domination redesign" of the control Lyapunov function (CLF) based Sontag's formula has been shown to possess robustness to static and dynamic input uncertainties. In this paper we provide a sufficient condition for the domination redesign to apply. This condition relies on properties of local homogeneous approximations of the system and of the CLF. We show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these conditions may guide the choice of a CLF which is suitable for domination redesign. © 1999 Elsevier Science B.V. All rights reserved.

Enduring Borderlands: the Marches of Ireland and Wales in the Early Modern Period

This joint chapter explores similarities and differences between two borderlands within the early modern ‘British’ state – the marches of Ireland and Wales. In some respects, the two regions were very different, most fundamentally because the Irish march remained militarised throughout the Tudor period, while Welsh society was markedly more peaceful. However, there was also much in common. In the later middle ages both marches were frontiers between the expanding Anglo-Normans and native Celtic society. The notion that the march separated ‘civility’ from ‘savagery’ was an enduring one: despite the efforts of the Tudors to impose centralisation and uniformity throughout its territories, there remained institutions, structures of power, and mentalities which ensured that both sets of marches were still in existence by the end of the 16th century. This chapter explores the reasons for the endurance of these borderlands, and indicates how political reforms of the 16th century caused the perception – and sometimes the very location – of the marches to alter.