Stabilization of Discrete-time 2-D T-S Fuzzy Systems Based on New Relaxed Conditions

This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Approximation methods of mixed l_1/H_2 optimization problems for MIMO discrete-time systems

The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.

2-D algebraic test for robust stability of time-delay systems with interval parameters

The robust stability test of time-delay systems with interval parameters can be concluded into the robust stability of the interval quasipolynomials. It has been revealed that the robust stability of the quasipolynomials depends on that of their edge polynomials. This paper transforms the interval quasipolynomials into two-dimensional （2-D） interval polynomials （2-D s-z hybrid polynomials）, proves that the robust stability of interval 2-D polynomials are sufficient for the stability of given quasipolynomials. Thus, the stability test of interval quasipolynomials can be completed in 2-D s-z domain instead of classical 1-D s domain. The 2-D s-z hybrid polynomials should have different forms under the time delay properties of given quasipolynomials. The stability test proposed by the paper constructs an edge test set from Kharitonov vertex polynomials to reduce the number of testing edge polynomials. The 2-D algebraic tests are provided for the stability test of vertex 2-D polynomials and edge 2-D polynomials family. To verify the results of the paper to be correct and valid, the simulations based on proposed results and comparison with other presented results are given.

Design of Discrete-time Repetitive Control System Based on Two-dimensional Model

This paper presents a novel design method for discrete-time repetitive control systems （RCS） based on two-dimensional （2D） discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality （LMI） method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.

Duality of 2-D singular systems of Roesser models

In this paper, the properties and concepts of dual systems of the two-dimensional singular Roesser models （2-D SRM） are studied. Two different concepts of the dual systems are proposed for the 2-D SRM. One is derived from the duality defined for two-dimensional singular general models （2-D SGM）-called the S-dual systems; the other one is defined based on 2-D SRM in a traditional sense-called the T-dual systems. It is shown that if a 2-D SRM is jump-mode free or jump-mode reachable, then it can be equivalently transformed into a canonical form of a 2-D SRM, for which the T-duality and the S-duality are equivalent. This will be of some perspective applications in the robust control of 2-D SRM.

Robust stability test for 2-D continuous-discrete systems with interval parameters

It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i. e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.

Robust Suboptimal Guaranteed Cost Control for 2-D Discrete Systems Described by Fornasini-Marchesini First Model

This paper considers the guaranteed cost control problem for a class of two-dimensional (2-D) uncertain discrete systems described by the Fornasini-Marchesini (FM) first model with norm-bounded uncertainties. New linear matrix inequality (LMI) based characterizations are presented for the existence of static-state feedback guaranteed cost controller which guarantees not only the asymptotic stability of closed loop systems, but also an adequate performance bound over all the admissible parameter uncertainties. Moreover, a convex optimization problem is formulated to select the suboptimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.

A Survey on the Stability of 2-D Discrete Systems Described by Fornasini-Marchesini Second Model

A key issue of practical importance in the two-dimensional (2-D) discrete system is stability analysis. Linear state-space models describing 2-D discrete systems have been proposed by several researchers. A popular model, called Forna- sini-Marchesini (FM) second model was proposed by Fornasini and Marchesini in 1978. The aim of this paper is to present a survey of the existing literature on the stability of FM second model.

LMI Approach to Suboptimal Guaranteed Cost Control for 2-D Discrete Uncertain Systems

This paper studies the problem of the guaranteed cost control via static-state feedback controllers for a class of two-dimensional (2-D) discrete systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model with norm bounded uncertainties. A convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the suboptimal guaranteed cost controller which ensures the quadratic stability of the closed-loop system and minimizes the associated closed-loop cost function. Application of the proposed controller design method is illustrated with the help of one example.

Non-Fragile Controller Design for 2-D Discrete Uncertain Systems Described by the Roesser Model

This paper is concerned with the design problem of non-fragile controller for a class of two-dimensional (2-D) discrete uncertain systems described by the Roesser model. The parametric uncertainties are assumed to be norm-bounded. The aim of this paper is to design a memoryless non-fragile state feedback control law such that the closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A new linear matrix inequality (LMI) based sufficient condition for the existence of such controllers is established. Finally, a numerical example is provided to illustrate the applicability of the proposed method.

Robust Non-Fragile Control of 2-D Discrete Uncertain Systems: An LMI Approach

This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.

Robust Optimal H∞ Control for Uncertain 2-D Discrete State-Delayed Systems Described by the General Model

This paper investigates the problem of robust optimal H∞ control for uncertain two-dimensional (2-D) discrete state-delayed systems described by the general model (GM) with norm-bounded uncertainties. A sufficient condition for the existence of g-suboptimal robust H∞ state feedback controllers is established, based on linear matrix inequality (LMI) approach. Moreover, a convex optimization problem is developed to design a robust optimal state feedback controller which minimizes the H∞ noise attenuation level of the resulting closed-loop system. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed method.

Output Feedback Robust H_(∞) Control for Discrete 2D Switched Systems

The two-dimensional(2-D)system has a wide range of applications in different fields,including satellite meteorological maps,process control,and digital filtering.Therefore,the research on the stability of 2-D systems is of great significance.Considering that multiple systems exist in switching and alternating work in the actual production process,but the system itself often has external perturbation and interference.To solve the above problems,this paper investigates the output feedback robust H_(∞)stabilization for a class of discrete-time 2-D switched systems,which the Roesser model with uncertainties represents.First,sufficient conditions for exponential stability are derived via the average dwell time method,when the system’s interference and external input are zero.Furthermore,in the case of introducing the external interference,the weighted robust H_(∞)disturbance attenuation performance of the underlying system is further analyzed.An output feedback controller is then proposed to guarantee that the resulting closed-loop system is exponentially stable and has a prescribed disturbance attenuation levelγ.All theorems mentioned in the article will also be given in the form of linear matrix inequalities(LMI).Finally,a numerical example is given,which takes two uncertain values respectively and solves the output feedback controller’s parameters by the theorem proposed in the paper.According to the required controller parameter values,the validity of the theorem proposed in the article is compared and verified by simulation.

Direct model reference adaptive control using K_p = LDU factorization for multivariable discrete-time plants

For a large class of discrete-time multivariable plants with arbitrary relative degrees, the design and analysis of the direct model reference adaptive control scheme are investigated under less restrictive assumptions. The algorithm is based on a new parametrization derived from the high frequency gain matrix factorization Kp=LDU under the condition that the signs of the leading principal minors of/fp are known. By reproving the discrete-time Lp and L2σ norm relationship between inputs and outputs, establishing the properties of discrete-time adaptive law, defining the normalizing signal, and relating the signal with all signals in the closed-loop system, the stability and convergence of the discrete-time multivariable model reference adaptive control scheme are analyzed rigorously in a systematic fashion as in the continuous-time case.

On the l_2-stability of time-varying linear and nonlinear discrete-time MIMO systems

New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.

δ-WAVE FOR 1-D AND 2-D HYPERBOLIC SYSTEMS

Here a new kind of nonlinear wave, which is called δ-wave, is described by some high resolution difference solutions for Riemann problems of one-dimensional (1-D) and two-dimensional (2-D) nonlinear hyperbolic systems in conservation laws. Some phenomena are numerically shown for the solutions of Riemann problems for 2-D gas dynamics systems

Robust state feedback for uncertain 2-D discrete switched systems in the Roesser model

The design of robust H_(∞)controllers is considered here for a class of two-dimensional(2-D)discrete switched systems described by the Roesser model with polytopic uncertainties.Attention focuses on the design of a switched state feedback controller,which guarantees the robust asymptotic stability and a prescribedH_(∞)performance for the closed-loop system.By using multiple parameter-dependent Lyapunov functionals,and introducing some switched free-weighting matrices,a new sufficient condition for the robust H_(∞)performance analysis of uncertain 2-D discrete switched systems is developed.Furthermore,the design of switched state feedback controller is proposed in terms of linear matrix inequalities(LMIs).Illustrative examples are given to illustrate the effectiveness of the developed theoretical results.

Novel plant activators with thieno[2,3-d]-1,2,3-thiadiazole-6-carboxylate scaffold: Synthesis and bioactivity

The 1,2,3-thiadiazole-carboxylate moiety was reported to be an important pharmacophore of plant activators.In this study,a series of novel plant activators based on thieno[2,3-d]-1,2,3-thiadiazole-6-carboxylate were designed and synthesized and their biological activity as plant activators was studied.The structures of the novel compounds were identifed by1H NMR,19F NMR and HRMS.The in vivo bioassay showed that these novel compounds had good effcacy against seven plant diseases.Especially,compounds 1a and 1c were more potent than the commercialized plant activator BTH.Almost no fungicidal activity was observed for the active compounds in the in vitro assay,which matched the requirements as plant activators.