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In this paper, the reconstruction error between the real system to be controlled and its T-S fuzzy model is considered in the context of control system design. As a result, an H∞ approach to adaptive controller that consists of two parts: one is obtained by solving certain linear matrix inequalities (LMIs) (fixed part) and another one is acquired by the fuzzy approximator in which the related parameters...
The paper presents results on stability analysis and controller synthesis of Takagi-Sugeno (T-S) fuzzy systems. A T-S fuzzy model is known to be usable in modeling and control of a wide range of nonlinear systems. In the paper, the multiple Lyapunov functions method is applied to formulate a sufficient condition for the stability of a T-S fuzzy system. Unlike previous approaches, the paper adopts...
This paper addresses the stabilization issue based on decentralized Static Output Feedback (SOF) non-Parallel-Distributed-Compensation (non-PDC) controllers for large scale nonlinear descriptors. The overall nonlinear plant is represented by interconnections between n Takagi-Sugeno (T-S) fuzzy descriptors. In order to avoid the appearance of crossing terms between local controllers and T-S subsystems,...
Robust stability analysis of a class of uncertain linear systems with time-varying delay is studied in this paper. In this system, the time-varying parameter uncertainty is norm-bounded and the delay is time-varying bounded function. Then, by using the method of LMI(Linear matrix inqulity) and Lyapunov stability theory, a sufficient and necessary condition for asymptotically stable expressed as LMI(Linear...
This paper is concerned with the stability analysis for systems with time-varying delay in a range. A new criterion of the delay-range-dependent stability is derived by introducing an appropriate type of Lyapunov functional with the idea of delay fractioning and is formulated in terms of a linear matrix inequality (LMI), which can be readily solved via standard software. This new criterion based on...
Fuzzy adaptive control method for uncertain nonlinear systems with time-delay is introduced in this paper, which can be represented by Takagi-Sugeno (T-S) fuzzy models. The state feedback approach is considered. By introducing a new Lyapunov-Krasovskii functional with adjustable parameters, and based on delay-dependent stability analysis, some sufficient conditions for the existence of state feedback...
For a class of linear sampled-data systems with norm-bounded uncertainty, sufficient conditions for the existence of state feedback control laws with the closed-loop poles in a pre-specified disk and optimizational robust H∞ performance are derived in terms of linear matrix inequalities (LMIs). The problem of designing the controllers with smaller gain parameters is formulated as a convex problem...
This paper pursues non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models through a local approach first proposed only for stability analysis. This solution overcomes the problem of dealing with time-derivatives of the membership functions (MFs) by reducing global stability goals to something less restrictive that leads to stabilization domains (local asymptotic conditions), which...
In this study, a stabilization problem for continuous-time fuzzy systems subject to multiple time-varying delays in both state and input variables is addressed. Based on Lyapunov-Krasovskii functional and Pólya theorem, a sufficient stabilization condition is stated in terms of LMIs. Therefore, stabilizing controllers can be obtained easily by existing convex algorithms. Unlike some existing methods,...
This paper discusses the problems of robust quadratic stability and robust H∞ control for a class of fuzzy descriptor systems with time-varying delay and parameter uncertainties. Base on the definition which is given by the Weihua Tian et al, according to the theory of Lyapunov, the sufficient conditions, which maintain the stability of the closed-loop and satisfy the H∞-performance are proved. These...
The robust decentralized connective stabilization problem for the expanding construction of large-scale systems, which is constituted by adding new subsystems one after another on the original construction during the operation, is considered in this paper. The problem is how to design the local control law of the new subsystem based on not changing the decentralized control laws of original construction,...
The robust H∞ output feedback control problem for uncertain discrete-time switched systems is investigated. A new linear matrix inequality(LMI) formulation of robustly stable and H∞ performance for the switched systems under arbitrary switching is obtained by using switched Lyapunov function method. The new LMI parameterized by a scalar variable which allows extra degree of freedom for design problems...
The observer-based static output feedback control problem for discrete-time switched systems is investigated. A sufficient condition of stability for the switched systems under arbitrary switching is obtained by using switched Lyapunov function approach. The linear matrix inequality (LMI) of the condition is parameterized by a scalar variable which allows extra degree of freedom for design problems...
This paper addresses a practical networked based control application. A Profibus DP is considered in order to coordinate a triangular maglev platform. The control of this magnetic levitation process is a complicated system from an control engineering point of view due to its unstable, non-minimum phase and non-linear nature; the difficulty is growing up because the bandwidth limitation and some other...
This paper investigates the problem of static output feedback stabilization for a class of uncertain discrete singular systems. Firstly, based on the stability criterion for the nominal discrete singular system, a sufficient condition for the existence of the static output feedback controller in terms of linear matrix inequality (LMI) with linear matrix equality (LME) constraint is established, which...
This paper is based on the stochastic linear quadratic (SLQ) control problem. The robustness of stabilizability of optimal controller for time-delay stochastic differential systems with Markov jumping parameters is investigated. Stochastic Lyapunov-Krasovskii functional, stochastic analysis, Ito formula, Schur complement and slack matrices are employed to analyze the exponential stability in mean...
This paper describes the dynamical uncertain systems by the Takagi-Sugeno (T-S) fuzzy dynamic model, and proposes a LMI design method of the robust fuzzy sliding mode observer by applying the robust sliding-mode observer design principle based on the singular value decomposition. Firstly, the Lyapunov function is used as the critical condition which ensures the consistent convergence of the designed...
This paper deals with the output feedback generalized H2 control for a class of discrete-time fuzzy systems with interval time-varying delay. Based on piecewise Lyapunov-Krasovskii functional, a LMIs characterization is established to guarantee the asymptotically stability and generalized H2 performance of the resulting closed-loop system. Explicit expressions of a desired output feedback controller...
This paper addresses robust stability of genetic regulatory networks (GRNs) with stochastic perturbation and discrete and distributed time-varying delays. Aside from discrete delays, there are few results about stability of GRNs with distributed delay. In this paper, noise perturbation and delays have been considered in both mRNA and protein dynamics. Based on Lyapunov functional approach and linear...
This paper discusses the problem of delay-dependent robust control for uncertain singular systems with time-delay. Firstly, based on Jensen inequality formula and Lyapunov stability theory, the sufficient condition is established for delay-dependent singular system with time-delay, which guaranteed the nominal system is regular, impulse free and stable. Secondly, based on the sufficient condition,...
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