Observer-based strict positive real (SPR) switching output feedback control

Abstract

This paper considers switching output feedback control of linear systems and variablestructure systems. Theory for stability analysis and design for a class of observer-based feedback control systems is presented. It is shown how a circlecriterion approach can be used to design an observerbased state feedback control which yields a closedloop system with specified robustness characteristics. The approach is relevant for variable structure system design with preservation of stability when switching feedback control or sliding mode control is introduced in the feedback loop. It is shown that there exists a Lyapunov function valid over the total operating range and this Lyapunov function has also interpretation as a storage function of passivity-based control and a value function of an optimal control problem. The Lyapunov function can be found by solving a Lyapunov equation. Important applications are to be found in hybrid systems with switching control and variable structure systems with high robustness requirements.

Switching control in blu-ray disk drives

“…This hampers the effectiveness of the switching when disturbances like shocks, vibrations and disk surface defects occur simultaneously. As a solution to the problem, a switching observer is studied [11,15]; regarding drive disturbances other approaches are given in [21,24]. Different however from the numerical (wafer stage) studies in [11] this paper considers the analysis, design, and demonstration of the switching observer applied to a blu-ray disk drive.…”

Model Matching and Passivation of MIMO Linear Systems via Dynamic Output Feedback and Feedforward

“…Interestingly, in the case of linear timeinvariant systems, these concepts are intimately related to the notion of Positive Real (PR) or of Strictly Positive Real (SPR) systems, which has been deeply explored not only in control but also in circuit theory, [2], [31], [32], [40]. In [18] a generalization of the Feedback Positive Real (FPR) design, introduced in [25], is discussed and subsequently extended to the setting of switching systems in [19]. The construction relies upon an observer-based state feedback control and on the circle criterion, thus increasing the realm of applicability of the solution proposed in [30], which yields a synthesis strategy in terms of a state feedback under the assumption that the underlying system is minimum-phase and possesses relative degree one.…”

Observer-based strictly positive real (SPR) variable structure output feedback control

“…Molander and Willems introduced a synthesis of state feedback control laws with a specified gain and phase margin [23], later extended to dynamic output feedback [24], [25]. In the context of hybrid control, a related result was presented [26].…”