Reduced-Order H ∞ Filters for Uncertain 2-D Continuous Systems,Via LMIs and Polynomial Matrices

This paper deals with designing H _∞ filters of reduced order for two dimensional (2-D) continuous systems described by Roesser models, with uncertain state space matrices. These filters are characterized in terms of linear matrix inequalities (LMI), to minimize a bound on the H _∞ noise attenuation, by using homogeneous polynomially parameter-dependent matrices of arbitrary degree. The methodology is also particularized for full order and zero order (static) filters, where more simple LMI conditions are derived. Numerical examples are presented to illustrate the proposed methodology.     

Improved results on observer-based control for discrete-time fuzzy systems

This paper is concerned with the design problem of observer-based H_∞ control for discrete-time Takagi?Sugeno (T?S) fuzzy systems. New sufficient conditions guaranteeing the H_∞ performance of the T?S fuzzy systems are derived. With the aid of some special derivations, bilinear matrix inequalities are converted into a set of linear matrix inequalities which can be solved using a single-step resolution procedure. In comparison with the existing literature results, the proposed approach may provide more relaxed conditions while ensuring better H_∞ performance. Finally, both numerical and practical examples are given to verify the effectiveness of the proposed approach.     

Stability of interval matrix polynomial in continuous and discrete cases

Sufficient conditions of asymptotic stability of interval matrix polynomial of both continuous and discrete cases are given. These conditions are presented in terms of the positive definiteness of either an (ln × ln) or (l × l) Hermitian and interval matrix. Therefore, the computation of the determinant interval polynomial is avoided.     

Constrained regulation of linear discrete-time systems with time delay: Delay-dependent and delay-independent conditions

The regulator problem is studied for discrete-time delay systems with asymmetrical constrained control. Necessary and sufficient conditions allowing us to obtain the largest asymmetrical polyhedral positively invariant with respect to the system in the closed loop are given. The case of symmetrical constrained control is obtained as a particular case. The results obtained can be divided into two categories. The first concerns the delay-independent positively invariant conditions and the second is the delay-dependent conditions.     

Stability Analysis and Robust H∞ Controller Synthesis with Derivatives of Membership Functions for T-S Fuzzy Systems with Time-varying Delay: Input-output Stability Approach

International Journal of Control, Automation and Systems - This paper investigates the problem of delay dependent stability and H∞ control design with derivatives of membership functions of...     

H ∞ Filtering of Two-Dimensional T-S Fuzzy Systems

The H _∞ filtering problem for two-dimensional Takagi–Sugeno fuzzy systems described by the Fornasini–Marchesini (FM) model is studied. Attention is focused on the design of an H _∞ fuzzy filter such that the filter error system is asymptotically stable and preserves a guaranteed H _∞ performance. By using basis-dependent Lyapunov functions and adding slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated. Then, a linear matrix inequality (LMI)-based approach is developed for designing the H _∞ fuzzy filter. Finally, an illustrative example is provided to show the effectiveness of the proposed approach and less conservatism.     

Improved stability and H∞ performance criteria for linear systems with interval time-varying delays via three terms approximation

This paper investigates the problem of delay dependent stability and H_∞ performance for a class of linear systems with interval time-varying delay. A new model transformation is first proposed by employing a three-terms approximation of delayed state variables, for a better approximation of delayed state. By using scaled small gain theorem and a simple Lyapunov–Krasovskii functional, new stability and H_∞ performance criteria are proposed in terms of linear matrix inequalities, which can be easily solved by using standard numerical packages. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.     

Further results on stability of

Our aim in this communication is to improve the existing results concerning the stability of . It is shown that the unstable characteristic roots could be more accurately located in a bounded and restrictive region of the complex plane. An iterative scheme is presented for numerical implementation of the results. Numerical computations are presented for illustration and comparison with previous results.