Shifting finite time stability and boundedness design for continuous-time LPV systems

In this paper, the problem of designing a parameter-scheduled state-feedback controller is investigated. In particular, the concepts of finite time stability (FTS) and finite time boundedness (FTB) are extended, introducing their shifting counterparts. By introducing new scheduling parameters, the controller can be designed in such a way that different values of these parameters imply different characteristics of the finite time stability/boundedness property. In this way, the performance of the control system can be varied during its operation. The problem is analyzed in the continuous-time LPV case, even though the developed theory could be also applied to LTI systems. The design conditions are feasibility problems involving linear matrix inequalities (LMIs) that can be solved efficiently using available solvers. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.

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