Design of parameter-scheduled state-feedback controllers using shifting specifications

In this paper, the problem of designing a parameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, H2 control and H∞ control problems, so as to satisfy new specifications, that will be referred to as shifting pole placement control, shiftingH2control and shiftingH∞control, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such a way that different values of these parameters imply different regions where the closed-loop poles are situated, or different performances in the H2 or H∞ sense. The proposed approach is derived within the so-called Lyapunov Shaping Paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, even though the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.