Analysis and design of parameter-dependent systems

Abstract

The structured uncertainty models presented in Chap. 9 are not the unique way to represent systems with uncertain parameters. These models are usually appropriate to describe systems whose uncertainties are relatively small in size and may not be convenient to implement in the case of large parameter variations. In such cases it might be better to use models in the form of the so called parameter-dependent systems which are appropriate for use in the more general case of large uncertainties. The linear parameter-dependent systems, called also Linear Parameter-Varying Systems (LPV systems), arise in many applications, for instance in robotics and aerospace systems. In this chapter we show how to build models of parameter-dependent systems and how to use these models in robust stability analysis and controller design. Especially important is the so called gain scheduling design, which allows to obtain satisfactory closed-loop performance in case of widely varying plant parameters.