Peak-to-Peak Gain Minimization for Uncertain Linear Discrete Systems： A Matrix Inequality Approach

为不明确的线性分离系统的一个班的 peak-to-peak 获得最小化的一条矩阵不平等途径被学习。我们最小化 * 是导致的 L 标准上的最好的上面的界限的 -norm, 由与逃避不了的椭圆体围住可达到的集合获得了，而不是直接最小化导致的 L 标准。基于这个想法，柔韧的 peak-to-peak 获得最小化的问题和控制器合成被归结为解决一套矩阵不平等的可行性问题。一个数字例子被用来表明介绍方法的可行性和有效性。

Controllability of Nonlinear Discrete Systems with Degeneracy

This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results.

Optimal Guaranteed Cost Control via Static Output Feedback for Uncertain Discrete Time Systems

Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods\ An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion\ Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.

Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices

The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.

Book Announcement of L. Celentano, Robust Tracking Controllers Design with Generic References for Continuous and Discrete Uncertain Linear SISO Systems, LAP LAMBERT Academic Publishing, 2012

In this book new results on controller design techniques for the tracking of generic reference inputs are presented. They allow the design of a controller for an uncertain process, either continuous or discrete-time, without zeros, and with measurable state. The controller guarantees that the control system is Type 1 and has the desired constant gain and poles or that the control system tracks, with a specified maximum error and with a specified maximum time constant, a generic reference with bounded derivative (variation in the discrete-time case), also in the presence of a generic disturbance with bounded derivative (variation). In addition, it is considered the case in which the reference is known a priori. The utility and the efficiency of the proposed methods are illustrated with attractive and significant examples of motion control and temperature control. This book is useful for the design of control systems, especially for manufacturing systems, that are versatile, fast, precise and robust.

Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.

Time domain analysis for discrete difference equation on discrete linear system controllable problem's research

We usually describle a comparatively more complex control system,especially a multi-inputs and multi-outputs system by time domation analytical procedure.While the system's controllability means whether the system is controllable according to certain requirements.It involves not only the system's outputs' controllability but also the controllability of the system's partial or total conditions.The movement is described by difference equation in the linear discrete-time system.Therefore,the problem of controllability of the linear discrete-time system has been converted into a problem of the controllability of discrete-time difference equation.The thesis makes out the determination method of the discrete-time system's controllability and puts forward the sufficient and necessary conditions to determine it's controllability by making a study on the controllability of the linear discrete-time equation.

Robust non-fragile control for discrete-delay nonlinear large-scale systems

Time-delays,due to the information transmission between subsystems,naturally exist in large-scale systems and the existence of the delay is frequently a source of instability. This paper considers the problems of robust non-fragile fuzzy control for a class of uncertain discrete nonlinear large-scale systems with time-delay and controller gain perturbations described by T-S fuzzy model. An equivalent T-S fuzzy model is represented for discrete-delay nonlinear large-scale systems. A sufficient condition for the existence of such non-fragile controllers is further derived via the Lyapunov function and the linear matrix inequality( LMI) approach. Simulation results demonstrate the feasibility and the effectiveness of the proposed design and the proper stabilization of the system in spite of controller gain variations and uncertainties.

Mixed Gl2／GH2 multi-channel multi-objective control synthesis for discrete time systems

This paper proposes a new approach for multi-objective robust control. The approach extends the standard generalized l2 (Gl2) and generalized H2 (GH2) conditions to a set of new linear matrix inequality (LMI) constraints based on a new stability condition. A technique for variable parameterization is introduced to the multi-objective control problem to preserve the linearity of the synthesis variables. Consequently, the multi-channel multi-objective mixed Gl2/GH2 control problem can be solved less conservatively using computationally tractable algorithms developed in the paper.

On Asymptotic Stabilization of Linear Discrete-time Systems with Saturated State Feedback

As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

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.

Feedback control design for discrete-time piecewise affine systems

This paper investigates the design of state feedback and dynamic output feedback stabilizing controllers for discrete-time piecewise affine(PWA) systems.The main objective is to derive design methods that will incorporate the partition information of the PWA systems so as to reduce the design conservatism embedded in existing design methods.We first introduce a transformation that converts the feedback control design problem into a bilinear matrix inequality(BMI) problem.Then,two iterative algorithms are proposed to compute the feedback controllers characterized by the BMI.Several simulation examples are given to demonstrate the advantages of the proposed design.

Decentralized H-infinity state feedback control for discrete-time singular large-scale systems

The decentralized H-infinity control problem for discrete-time singular large-scale systems is considered. Based on the bounded real lemma of discrete-time singular systems, a sufficient condition for the existence of decentralized H-infinity controller for discrete-time singular large-scale systems is presented in terms of the solvability to a certain system of linear matrix inequalities by linear matrix inequality (LMI) approach, and the feasible solutions to the system of LMIs provide a parameterized representation of a set of decentralized H-infinity controller. The given example shows the application of the method.

Improved Results on Robust H_∞ Control of Uncertain Discrete-time Systems with Time-varying Delay

In this paper, the robust H∞ control problem for uncertain discrete-time systems with time-varying state delay is con- sidered. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional, a new less conservative sufficient condition for the existence of a robust H∞ controller is obtained. Moreover, the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem. Finally, several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Robust Stabilization of Nonlinear Time Delay Discrete-time Systems Based on T-S Model

A robust stabilization problem is considered for time delay nonlinear discrete-time systems based on T-S fuzzy model. A necessary and sufficient condition for the existence of such controllers is given through Lyapunov stability theorem. And it is further shown that this condition is equivalent to the solvability of a certain linear matrix inequality, which can be solved easily by using the LMI toolbox of Matlab. At last, an illustrative example of truck-trailer is presented to show the feasibility and effectiveness of the proposed method.

Adaptive control for a class of discrete-time time-delay systems with regard to delay parameter

The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our designed adaptive control law, the unknown time-delay parameter is included in memory state feedback controller. Using LMI technique, delay-dependent sufficient conditions for the existence of the feedback controller are obtained. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example.

Novel l_2-l_∞ controller design for LPV discrete time-delay systems

One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present a parameter-dependent l 2-l ∞ performance criterion using a parameter-dependent Lyapunov function. Upon the conditions addressed, an improved parameter-dependent l 2-l ∞ performance criterion is established by the introduction of a slack variable, which exhibits a kind of decoupling between Lyapunov functions and system matrices. This kind of decoupling enables us to obtain more easily tractable conditions for analysis and synthesis problems. Then, the corresponding parameter-dependent state-feedback controller design is investigated upon these performance criteria, with sufficient conditions obtained for the existence of admissible controllers in terms of parameterized linear matrix inequalities. Finally, a numerical example is provided to illustrate the feasibility and advantage of the proposed controller design procedure.

Delay-dependent robust H-infinity control for discrete-time uncertain systems with time-varying state delays

This paper examines the delay-dependent H-infinity control problem for discrete-time linear systems with time-varying state delays and norm-bounded uncertainties. A new inequality for the finite sum of quadratic terms is first established. Then, some new delay-dependent criteria are derived by employing the new inequality to guarantee the robust stability of a closed-loop system with a prescribed H-infinity norm bound for all admissible uncertainties and bounded time-vary delays. A numerical example demonstrates that the proposed method is an improvement over existing ones.