Linear Matrix Inequality

This paper deals with the robust sliding mode control of a brushless d.c. motor drive. A state-space model of the system is developed. The sliding mode controller is separated into linear and non-linear components. The novelty of the approach is in the rationale and method used to synthesize the linear control component which involves a linear matrix inequality (LMI) optimization. System uncertainty due to changes in load inertia is represented as norm bounded. A robust design approach is developed, yielding a robust controller against system uncertainties. A reaching condition to bring the system states to a sliding surface is developed, and the control burden lies heavily on the linear part to alleviate the chattering problem of conventional sliding mode control. The effect of the non-linear component on system performance is analysed. Testing the proposed controller verifies its effectiveness compared with the conventional one.

In this paper, stabilization of an Active Magnetic Bearing (AMB) system with varying rotor speed using Sliding Mode Control (SMC) techniques are considered. The gyroscopic effect and imbalance inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Also, transformation of the AMB dynamic model into a

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semi-partitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered complete Heyting algebra, we construct an algorithm for calculation of a minimal family of its equivalence classes which generates it. Most of the presented results are new, but some of them are generalizations of known results given in a way which simplifies and clarifies them.

This paper studies a time-delayed decentralized structural control strategy that aims to minimize the H2 norm of the closed-loop system. In a decentralized control system, control decisions are made based on data acquired from sensors located in the vicinity of a control device. Due to the non-convexity nature of the optimization problem caused by a decentralized architecture, controller design for decentralized systems remains a major challenge. In this work, a homotopy method is employed to gradually transform a centralized controller into multiple decentralized controllers. Linear matrix inequality (LMI) constraints are adopted in the homotopic transformation to ensure closed-loop control performance. In addition, multiple decentralized control architectures are implemented with a network of wireless sensing and control nodes. The sensor network allows simultaneous operation of multiple wireless subnets. Both the theoretical development and system implementation support the information overlapping between decentralized subnets. For validation, the wireless sensing and control system is installed on a six-story laboratory steel structure controlled by magnetorheological (MR) dampers. Shake-table experiments are conducted to demonstrate the performance of the wireless decentralized control strategies.

Describes a direct way to solve the robust output feedback stabilization problem for a class of uncertain nonlinear systems with nonlinear parameterization using the backstepping technique. The backstepping method is performed in a batch way rather than recursively. The paper begins with the stabilization of a system containing a series of integrators with unknown gains. The solution of the problem is then used to solve the output feedback stabilization problem of the nonlinear system

Articles Articles, All fields, Author, Advanced search. Images Images, Journal/Book title, Volume, Issue, Page, Search tips. ... Technical Communique. A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays ☆. ...

In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities (LMIs) to study the global asymptotic stability of state-delay systems. Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a pH neutralizing process are provided to demonstrate the efficacy of the proposed method.

This paper investigates the stability of fuzzy-model-based (FMB) control systems. An alternative stability-analysis approach using an artificial fuzzy system based on the Lyapunov stability theory is proposed. To facilitate the stability analysis, the continuous membership functions of the Takagi-Sugeno (T-S) fuzzy model are represented by the staircase ones. With the nice property of the staircase membership functions, it turns the set of infinite number of linear-matrix-inequality (LMI) based stability conditions into a finite one. Furthermore, the staircase membership functions carrying system information can be brought to the stability conditions to relax the stability conditions. The stability of the original FMB control systems is guaranteed by the satisfaction of the LMI-based stability conditions. The proposed stability analysis is applied to the FMB control systems of which the T-S fuzzy model and fuzzy controller do not share the same premise membership functions and, thus, is able to enhance the design flexibility of the fuzzy controller. A simulation example is given to illustrate the merits of the proposed approach.