Analysis and control of linear-parameter-varying systems

The area of the analysis and control of linear parameter-varying (LPV) systems has received much recent attention because of its importance in developing systematic techniques for gain-scheduling. An LPV system resembles a linear system that nonlinearly depends on time-varying parameters.; Typical approaches for the analysis and control of LPV systems are the scaled small-gain and the dissipative systems approach using smooth parameter-dependent Lyapunov functions (PDLFs). The dissipative systems approach is the more desirable of the two techniques because it can directly treat time-varying parameters. and yield a general LPV-type controller. Furthermore, this approach attractively formulates analysis and synthesis problems as convex optimization problems involving linear matrix inequalities (LMIs) which are now very efficiently solved by computer. However, this approach has two major potential difficulties in selecting an optimal PDLF in order to reduce conservatism of the analysis and synthesis, and solving exactly convex optimization problems involving an infinite number of LMIs.; The thesis presents new analysis and control design techniques to avoid these potential drawbacks of the smooth dissipative systems approach. The thesis focuses on a piecewise-affine parameter-dependent linear parameter-varying system and a nonsmooth piecewise-affine parameter-dependent Lyapunov function. To address the non-differential nature of both the LPV system and PDLF, the thesis develops a nonsmooth dissipative systems framework. Then the thesis fully characterizes several important analysis and synthesis problems of LPV systems with this nonsmooth framework.; The new approach is shown to yield a less conservative, guaranteed result than previously published LPV approaches. The improvement is direct results of using a more accurate model in the analysis and control, and using a very general class of PDLFs. The derived analysis and synthesis formulations are finite-dimensional convex optimization problems. The new approach also provides a trade-off between conservatism and computational effort of the design technique. Several benchmark problems are used to demonstrate the usefulness, reliability, and feasibility of the proposed new approaches.