| The work presented here considers the control of linear parameter-varying (LPV) systems involving real, time-varying parameters. The control objectives are internal stability and disturbance rejection in the sense of an induced ;Firstly, a new characterization of ;Next, parameter-independent control of LPV systems is investigated. In contrast to the parameter-dependent control, the existence conditions for parameter-independent controllers define a non-convex optimization problem expressed in terms of two LMI's, coupled with an additional nonlinear condition, which destroys convexity. However, it is shown that when certain assumptions on the system matrices are satisfied, a two-step sequential solution of the solvability conditions (which essentially turns the original non-convex problem into a convex one) is possible. For the more general case where no assumptions are made on the system matrices, the "troublesome" nonlinear condition is transformed into a rank constraint and an iterative rank-minimization approach (which involves LMI's only) is proposed for checking the feasibility of the solvability conditions.;Finally, the results of the previous chapters are combined and the design of controllers that depend only on some of the parameters in the system is considered. The solvability conditions for such controllers are also expressed in terms of LMI's in addition to a non-convex constraint. Therefore, the rank-minimization approach proposed in the previous chapter is extended to this case. Examples that demonstrate the applicability of the results are given. |
