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This paper addresses the local stability analysis problem for continuous-time Takagi–Sugeno (T–S) fuzzy systems. Based on the Lyapunov method, the proposed analysis procedure is formulated as optimizations subject to linear matrix inequalities (LMIs) which can be solved by means of convex optimization techniques. Especially, a generalized Lyapunov function that depends on the membership functions (MFs) and its time derivatives is used. Since the Lyapunov function involves the time derivatives of the MFs, the problem of stability analysis and the estimation of the domain of attraction (DA) cannot be converted into convex problems in general. In this paper, we explore the possibility of using the second-order time derivatives of the MFs to determine the DA. Examples are given to illustrate the proposed method.

Recently, the so-called FIR-type (FIR, finite impulse response) state-feedback memory controller and periodic memory controller have been developed, and it was revealed that this control design approach can reduce the conservatism of stability and stabilization conditions for periodic or uncertain systems. In these work, the system duality and a descriptor representation of the original system are used. In this paper, we focus only on the FIRtype state-feedback memory controller design problem, which is a special case of the general memory controller structure previously developed. Although the structure of the controller considered in this paper is a particular case of the existing one, this special consideration gives some benefits, which are the main purpose of this paper. Finally, examples demonstrate the effectiveness of the FIR-type state-feedback memory controller in terms of less conservatism.

In this paper, we propose an iterative linear matrix inequality (LMI) approach to design static output feedback (SOF) controllers for continuous-time linear time-invariant (LTI) systems. The method suggested in this paper can be viewed as a version of some previous iterative LMI methods. Although the proposed method cannot always provide improved results in comparison with the previous one, it can be used as a less conservative alternative in some cases. In addition, it can be combined with the previous algorithm to improve the results. Finally, an example is gSiven to demonstrate the validity of the proposed methods.

The goal of this paper is to propose linear matrix inequality (LMI) formulations to analyze the local stability and local stabilization of discrete-time nonlinear systems represented by Takagi–Sugeno (T–S) fuzzy systems with time-delay. In order to estimate the domain of attraction (DA) of the time-delay systems, the so-called fuzzy Lyapunov-Krasovskii functionals are used to characterize the subsets of the DA as sublevel sets of the Lyapunov- Krasovskii functionals. We use the information of the variation rates of the membership functions to obtain less conservative results. Finally, examples are given to illustrate the proposed methods.

This paper addresses local H ∞ controller design problems for continuous-time Takagi–Sugeno (T–S) systems with magnitude- and energy-bounded disturbances. The design procedure is formulated as optimizations subject to linear matrix inequalities (LMIs) which can be solved by means of convex optimization techniques. The designed controllers not only guarantee the H ∞ performance but also ensure the state not to escape an invariant set that is included by the region where the T–S fuzzy model is defined. Finally, an example is given to illustrate the proposed method.

In this paper, robust H 2 and H ∞ control problems for discrete linear time-invariant (LTI) systems with polytopic uncertainties are addressed. The so-called finite impulse response (FIR) controller incorporating the states over several samples from the past to the present is adopted to design robust control laws with improved performances. For the closed-loop stability, parameter-dependent quadratic Lyapunov functions (PD-QLFs) are employed. Sufficient controller synthesis conditions are derived in the form of linear matrix inequalities (LMIs). Finally, examples are given to demonstrate the usefulness of the proposed methods.

In this paper, we propose linear matrix inequality (LMI) formulations to analyze local stability and design controllers that locally stabilize continuous-time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy systems. In order to estimate the domain of attraction (DA), the so-called fuzzy Lyapunov function is used to characterize the subsets of the DA as sublevel sets of the Lyapunov function. Quadratic bounds on the time-derivative of the membership functions are employed to derive the main results. Finally, examples are given to illustrate the proposed methods.

The so-called digital redesign (DR) is a sampled-data (SD) controller design method where an analogue controller is designed firstly, and then transformed to an approximately equivalent digital controller in the sense of state-matching. In this approach, the SD controller is designed by reducing the discrepancy between the discrete-time (DT) counterpart of the closed-loop SD control system and the continuous-time (CT) closed-loop system. In this paper, we develop a DR strategy for CT linear time-invariant systems. More specifically, H∞ norm of the error dynamic system between the CT and DT plants is minimized for the optimal state-matching performance at every sampling point. The design problem is formulated as linear matrix inequalities which can be efficiently solved by using convex optimization techniques. Finally, an example is given to illustrate the effectiveness of the proposed method.

For continuous-time linear time-invariant (LTI) systems with polytopic uncertainties, we develop a robust sampled-data state-feedback control design scheme in terms of linear matrix inequalities (LMIs). Truncated power series expansions are used to approximate a discretized model of the original continuous-time system. The system matrices obtained by using the power series approximations are then expressed as homogeneous polynomial parameter-dependent (HPPD) matrices of finite degrees, and conditions for designing the controller are formulated as a HPPD matrix inequality, which can be solved by means of a recent LMI relaxation technique to test the positivity of HPPD matrices with variables in the simplex. To take care of the errors induced by the remainder terms of the truncated power series, the terms are considered as norm bounded uncertainties and then incorporated into the proposed LMI conditions. Finally, examples are used to illustrate the approach.

In this paper, a sufficient linear matrix inequality (LMI) condition is presented for robust stability analysis of continuous-time linear time-invariant (LTI) systems in polytopic domains. The underlying idea behind the proposed approach is to introduce a family of complex functions which map the closed right-hand side of the complex plane into the inside of the closed unit circle centered at the origin. Then, the mapping properties are used to assure that all the eigenvalues of a system are located in the open left-hand side of the complex plane. Examples show the validity of the proposed condition.

In this paper, a systematic procedure to design the robust H ∞ fuzzy controller for a nonlinear active magnetic bearing (AMB) system affected by time-varying parametric uncertainties is presented. First, the continuous-time Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear AMB system. Next, based on the obtained fuzzy model, sufficient conditions are derived in terms of linear matrix inequalities (LMIs) for robust stability and H ∞ performance of the control system. The main feature of this paper is that some drawbacks existing in the previous approaches such as truncation errors and nonconvex bilinear matrix inequality (BMI) problem are eliminated by utilizing the homogeneous fuzzy model which includes no bias terms in the local state space models rather than the affine one which includes bias terms. Hence, the design method presented here will prove to be more tractable and accessible than the previous ones. Finally, numerical simulations demonstrate the effectiveness of the proposed approach.