Control of linear parameter varying systems

In this thesis we study the control problem of linear parameter varying (LPV) systems using LPV controllers. The LPV plants are finite-dimensional linear systems with known, parameter-dependent state-space data. The parameter is assumed measurable in real-time and varies in a known, bounded set. Our study is motivated by the gain-scheduling design method, and our results constitute a new approach to gain-scheduling.; Our design goal is: formulate a performance measure for an LPV system; develop computable bounds for the performance measure; determine conditions for the existence of a parameter-dependent controller so that the closed-loop system has suitable performance, or determine that no suitable controller exists. We aim for theorems that express conditions as the (in)feasibility of linear matrix inequalities (LMIs), which is a convex decision problem.; The first problem involves LQG performance for LPV systems, and is analogous to the standard {dollar}{lcub}cal H{rcub}sb2{dollar} performance for LTI and LTV systems. We give two analysis theorems (as LMIs) to bound the LQG performance of LPV systems. These bounds are less conservative than those in the current literature. For control synthesis, we consider two controllers: a parameter-dependent controller and a parameter-dependent state-feedback controller with optimal (Kalman) filter. We use convex optimization to reduce the performance bound of the closed-loop system.; Next, we investigate the induced L{dollar}sb2{dollar}-norm control of LPV systems which have bounded parameter variation rates and real-time measurement of the parameter and its derivative. Previous L{dollar}sb2{dollar}-gain LPV research used a single quadratic Lyapunov function for analysis, leading to conservatism in achievable performance. To remedy this, we employ parameter-dependent Lyapunov functions, and develop an efficient bound on the induced L{dollar}sb2{dollar}-norm by exploiting the known bound on the parameter's rate of variation. We then formulate the necessary and sufficient conditions for the existence of an LPV controller that renders this bound less than 1. The conditions are three LMI constraints on positive definite matrix functions of the parameters, resulting in an infinite dimensional convex feasibility problem. By parameterizing a subspace of the function space with a finite number of basis functions, the solvability condition is (approximately) converted to a finite-dimensional convex problem.