Synthesis of Decentralized Variable Gain Robust Controllers for Large-Scale Interconnected Systems with Structured Uncertainties

In this paper, we propose a decentralized variable gain robust controller which achieves not only robust stability but also satisfactory transient behavior for a class of uncertain large-scale interconnected systems. For the uncertain large-scale interconnected system, the uncertainties and the interactions satisfy the matching condition. The proposed decentralized robust controller consists of a fixed feedback gain controller and a variable gain one determined by a parameter adjustment law. In this paper, we show that sufficient conditions for the existence of the proposed decentralized variable gain robust controller are given in terms of LMIs. Finally, a simple numerical example is included. 1. Introduction To design control systems, it is necessary to derive a mathematical model for controlled systems. However, there always exist some gaps between the mathematical model and the controlled system; that is, uncertainties between actual systems and mathematical models are unavoidable. Hence for dynamical systems with uncertainties, so-called robust controller design methods have been well studied in the past thirty years, and there are a large number of studies for linear uncertain dynamical systems (e.g., see [1, 2] and references therein). In particular for uncertain linear systems, several quadratic stabilizing controllers and one have been suggested (e.g., [3–5]), and a connection between control and quadratic stabilization has also been established [6]. In addition, several design methods of variable gain controllers for uncertain continuous-time systems have been shown (e.g., [7–9]). These robust controllers are composed of a fixed gain controller and a variable gain one, and variable gain controllers are tuned by updating laws. Especially, in Oya and Hagino [8] the error signal between the desired trajectory and the actual response is introduced and the variable gain controller is determined so as to reduce the effect of uncertainties. On the other hand, the decentralized control for large-scale interconnected systems has been widely studied, because large-scale interconnected systems can be seen in such diverse fields as economic systems, electrical systems, and so on. A large number of results in decentralized control systems can be seen in ？iljak [10]. A framework for the design of decentralized robust model reference adaptive control for interconnected time-delay systems has been considered in the work of Hua et al. [11] and decentralized fault tolerant control problem has also been studied [12]. Additionally, there are many existing results