Analysis and Control of Linear Parameter-varying Systems

The area of 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 one or more time-varying parameters. Nonlinear systems are often modeled in the LPV system via the parameterized Jacobian linearization. Typical approaches for the analysis and control of LPV systems are the scaled smallgain approach and the dissipative systems framework using smooth parameter-dependent Lyapunov functions (PDLFs). The dissipative systems framework is the more desirable of the two techniques because it can directly treat time-varying parameters and yield an LPVtype controller. Furthermore, the dissipative systems framework attractively formulates analysis and synthesis problems as convex optimization problems involving linear matrix inequalities (LMIs), which are now very e ciently solved by computer. However, the current dissipative systems framework has two major potential drawbacks: (1) di culty in selecting an optimal PDLF in order to reduce conservatism of the dissipative systems approach; (2) di culty in solving exactly convex optimization problems involving an in nite number of LMIs. The thesis presents new analysis and control design techniques to avoid these potential drawbacks of the smooth dissipative systems framework. The thesis focuses on a piecewise-a ne parameter-dependent linear parameter-varying (PALPV) system which is a new class of LPV systems. Associated with the PALPV system is a piecewise-a ne parameter-dependent Lyapunov function (PAL). To address the non-di erential nature of both the PALPV system and the PAL, the thesis develops a nonsmooth dissipative systems framework. Then, the thesis fully characterizes several interesting analysis and synthesis problems, such as L2-gain, L1-gain, H2-norm, passivity, and robust counterparts, of PALPV system with the developed nonsmooth dissipative systems framework.