Quadratic stability and performance of linear parameter dependent systems

In this thesis a parameter dependent control problem for linear parametrically varying (LPV) plants is studied. LPV systems are finite dimensional linear systems whose state-space entries depend on one or more time-varying parameters. It is assumed that these parameters are measured in real time and are thus available to the controller. It is also assumed that these parameters are contained in some (possibly large) bounded set that is known a priori. No additional information about the parameters is assumed. The study of such systems is motivated by gain scheduling, an ad hoc design methodology that is extensively used in industry. The control of LPV systems differ fundamentally from that of standard linear time varying systems because the time variation of the LPV system is not known beforehand.Measures of stability and performance for LPV systems are defined in terms of a single quadratic Lyapunov function. Sufficient conditions that guarantee an LPV system is exponentially stable and achieves an induced LControl synthesis problems for LPV systems are also addressed. Necessary and sufficient conditions for an LPV system to be exponentially stabilizable by a linear parametrically dependent controller are derived. The set of linear parametrically dependent controllers which yield closed-loop exponential stability are characterized by a Youla parametrization. Additionally, necessary and sufficient conditions are presented which establish the existence of a linear parameter dependent controller that renders the closed loop system exponentially stable and achieves a performance level (measured by the L...