Decentralised output‐feedback controller syntheses with restricted frequency‐domain specifications via generalised Kalman–Yakubovich–Popov lemma: a unified approach

Abstract

This study is concerned with output-feedback H-infinity controller synthesis in finite frequency domain for continuous-time multi-channel linear systems. The recently developed results of full-order centralised H-infinity control theory in this field are extended to the subject of decentralised control. Both the block-diagonal reduced-order dynamic and static controller designs are discussed in a unified manner. Sufficient solvability conditions are given in terms of linear-matrix-inequalities. A numerical example is provided that establishes the efficacy of the proposed controller syntheses. IntroductionRecently there is a renewed interest in the field of H-infinity loop shaping [1] in which the design objective is to synthesise a stabilising controller to fulfil multiple frequency domain specifications set on various restricted frequency ranges. A novel approach capable of achieving this goal without introducing weighting functions into its design procedure has been developed. This approach is based on the so called generalised Kalman-Yakubovich-Popov (GKYP) lemma [2], initiated by the pioneer work of Iwasaki and his collaborators [3] in 2000. In recent years more and more theoretical results pertinent to this powerful tool have been established, for example model reduction [4], computation issues [5] and feedback controller synthesis [6-10], to name a few. On the other hand, an increasing number of engineering applications have been explored in diverse fields, for examples, disturbance rejection [11], track following control [12], active suspension systems [13, 14], fault detection [15], fuzzy filter design [16], quantisation noise reduction in uncertain cascaded sigma-delta modulators [17] and image coding [18].Focusing on the topic of feedback control synthesis in this field, to the best of the author's knowledge, the existing results (derived via the GKYP lemma) deal with either single-input-single-output cases or provide only centralised controller designs for multi-inputmulti-output systems. There has not yet an article of this field addressing structural control design. This motivates us to devote ourselves to this problem.On the subject of decentralised H-infinity control, in sharp contrast with the absence of work in the field of finite frequency decentralised control, there are profound results in the full frequency domain, see for example [19][20][21][22][23][24][25] and the references therein. Two major problem formulations have been addressed in literature. A typical class of problems deal with designing a decentralised stabilising controller such that a certain closed-loop transfer function satisfies a given H-infinity performance level over the entire frequency range (see e.g. [19-21] and references therein) or determining optimal decentralised H-infinity controllers under the so-called quadratic invariance assumption (see e.g. [22,23] and references therein). In the second class of problems the aforementioned problem is considered with an additional order constraint imposed upon the local contro...

Robust fault estimation in the finite-frequency domain for multi-agent systems

“…Iwasaki and Hara (2005) proposed the generalized Kalman–Yakubovich–Popov (GKYP) lemma which provided the linear matrix inequalities (LMIs) condition for finite-frequency domain performance. There is a rich literature on control design in the finite-frequency domain to avoid possible conservatism and the overdesign problem (Chou and Chang, 2015; Iwasaki and Hara, 2007; Li and Gao, 2015). In recent years, some researchers have used the GKYP lemma to reduce conservativeness in FD design conditions (Chen and Cao, 2013; Wang et al, 2017a,b; Yang et al, 2011; Zhai et al, 2016).…”