Static output feedback control for discrete-time fuzzy bilinear system

The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.

Delay-dependent static output feedback control of nonlinear system

The static output feedback control problem for time-delay nonlinear system is studied based on T-S fuzzy bilinear model. The objective is to design a delay-dependent static output feed- back controller via the parallel distributed compensation （ PDC ） approach such that the closed-loop system is delay-dependent asymptotically stable. A sufficient condition for the existence of such a controller is derived via the linear matrix inequality （LMI） approach and the design problem of the fuzzy controller is formulated as an LMI problem. The simulation examples show the effectiveness of the proposed approach.

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.

Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality （LMI） variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

LMI-based output feedback fuzzy control of chaotic system with uncertainties

This paper studies the robust fuzzy control for nonlinear chaotic system in the presence of parametric uncertainties. An uncertain Takagi-Sugeno （T-S） fuzzy model is employed for fuzzy modelling of an unknown chaotic system. A sufficient condition formulated in terms of linear matrix inequality （LMI） for the existence of fuzzy controller is obtained. Then the output feedback fuzzy-model-based regulator derived from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system. The T-S fuzzy model of the chaotic Chen system is developed as an example for illustration. The effectiveness of the proposed controller design methodology is finally demonstrated through computer simulations on the uncertain Chen chaotic system.

基于LMI的分段线性系统共存吸引子转迁控制研究

以一类两自由度含间隙分段线性系统为研究对象,利用线性矩阵不等式(linear matrix inequality,LMI)和线性反馈方法对系统共存的吸引子进行在预期目标轨道引导下的转迁控制。在状态平面上利用胞映射方法对系统随参数变化时的共存吸引子进行识别,并基于Poincaré映射和Lyapunov指数研究了系统共存吸引子的稳定性及转迁机理。基于LMI和Lyapunov理论,并利用系统的向量场信息和S-procedure,将系统施加线性反馈控制器后的稳定性和反馈增益矩阵的求解问题转化为LMI描述。利用数值方法验证了所应用的线性反馈控制器及其增益矩阵选取方法的可行性及正确性。

New synthesis algorithm of static output feedback sliding mode control for a class of uncertain systems

Based on a kind of regular form, a Lyapunov matrix with special structure is presented to design the sliding surface matrix conveniently and then an effective algorithm is developed on it. A simple static output feedback sliding mode control law without extra dynamic equation is given, such that the predefined sliding surface is reached in finite time for the general matching uncertainties. In the reported result, this extra dynamic equation is used for evaluating the norm bound of the unmeasured state vector. Finally, some examples are studied to illustrate the proposed approach.

Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions

The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.

LMI_based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.

Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.

基于LMI的不确定随机时滞系统输出反馈保性能控制

针对一类范数有界的随机时滞系统,研究在一定性能指标下的保性能控制问题。本文为获得能够实现系统保性能控制的最优输出反馈控制器,采用Lyapunov稳定性理论与LMI技术相结合的方法,将保性能控制问题转化为LMIs约束下的可行解问题。提出的控制器设计方案能够实现系统是依概率全局渐近稳定的,同时满足对系统性能指标的要求。此外,通过数值算例说明所提出控制方案的可行性。

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

基于LMI的不确定混沌系统的模糊输出反馈控制

研究了基于 T-S 模糊模型描述的不确定混沌系统的静态输出反馈鲁棒控制问题,给出一种新的模糊静态输出反馈控制器设计方法。该方法充分考虑了模糊子系统间的相互作用,静态输出反馈控制器可通过求解一组线性矩阵不等式(LMI)获得。为说明问题,给出了 Chen 混沌系统模糊静态输出反馈控制设计和仿真结果。

基于LMI双故障动态输出反馈完整性控制

针对线性系统,基于线性矩阵不等式(LMI)给出了具有完整性的动态输出反馈控制器的设计方案,所得到的结论,不仅给出分别考虑执行器和传感器两类部件发生故障的完整性设计方案,而且给出了考虑执行器或传感器任何一类部件发生故障的完整性设计方案．本文使用了比离散故障模型更具有实际意义的连续故障模型．一个数值例子说明了所提方法的有效性．

基于LMI的分布时滞系统输出动态反馈镇定

研究分布时滞系统的输出动态反馈镇定问题.基于闭环系统的中立型变换及相应Lyapunov-Krasovskii泛函的构造与解析技巧,建立了与时滞相关的控制器存在性判据.在此基础上通过控制器参数化设计方法,将控制器参数的求解归结为线性矩阵不等式解的形式.仿真算例验证了方法的有效性。

基于LMI的主动悬架的滚动时域H∞输出反馈控制

以2自由度1/4车辆的悬架动力学模型为研究对象,提出滚动时域H∞输出反馈控制策略。利用在线最小化H∞性能指标,设计控制器,协调相互冲突的诸性能要求。仿真结果表明,系统在保证满足约束的前提下可以尽可能地降低干扰对输出的影响,获得优化的动态性能指标。