A contraction property for state feedback design of linear discrete-time systems

This paper is concerned with the method of impulsive controller design for linear systems with multiple-packet transmission. First, the mathematic model of respond closed-loop is built in terms of linear impulsive systems description. Second, on the basis of guaranteeing closed loop systems stability, the design method of the impulsive feedback controller and the design procedure are given. Finally, numerical simulation is provided to demonstrate that asymptotically stability of close-loop linear uncertainly impulsive system with multiple-packet transmission is guaranteed by using the impulsive controller.

This paper concerns the problems of robust stability analysis and stabilization for uncertain linear system with time-varying delay. In order to obtain a robust stability criterion with less conservative for uncertain linear delay system, a quadratic integral inequality is improved by matrix decomposition. Further, two different kinds of controller, i.e., linear memoryless state feedback controller and linear state feedback controller with state delay, are derived in terms of the robust stability criteria. Two numeral examples are provided to demonstrate the validity of the proposed methods.

In this paper a basis is developed for the systematic design of linear multivariable discrete-time tracking systems for plants with inaccessible states, which thus extends the results for discrete-time plants with accessible states previously obtained by Bradshaw and Porter (1975). The design method is illustrated by the presentation of the results of computer simulation studies.

This paper considers a subclass of hybrid systems, which is the discrete-time linear switching systems whose changes in the dynamics are determined by exogenous, uncontrollable events, and resets are present. In the presence of uncertain parameter and non-symmetrical constrained control, based on the results of nominal linear switching systems, a necessary and sufficient condition to test the robustness of a state feedback controller is given. The candidate state feedback controller for this test is that stabilizing nominal discrete-time linear switching systems. Also, the method in this paper can be extended to the case which has state constraints. At last, a numerical example is presented to illustrate the technique.

Traditionally, corrections for linear control systems are always based on precise drawing of root locus or Bode plot of the linear systems, requiring fussy trying again and again, but not necessarily giving satisfying correction results. Combining analytic geometry with root locus method, this paper introduced a calculation method for series lagging correction. Without precise drawing of root locus of the system and fussy trying, this method gives precise and satisfying correction results, providing a simple but effective route to the designing of linear control systems. It also establishes another groundwork for simulating the design of linear control systems using computers.KeywordsRoot LocusSeries Lagging CorrectionCalculation Method

This paper studies the design of uncertain linear discrete-time Networked Control Systems over imperfect communication channels with time-varying data loss. This leakage is modeled as stochastic parameter and norm-bounded uncertainties. In addition, this paper defines the necessary conditions for the design of the dynamic output feedback controller; subsequently, an iterative LMI approach is specified to compute the controller state parameters. The simulation results show that the designed controller improves the H∞ disturbance attenuation performance of the concerned uncertain system.

The paper is concerned with the problem of feedback control law design in the form of PS output controller for linear discrete-time systems. Since these tasks generally make towards bilinear optimization problems, using the standard quadratic form of Lyapunov function and a symmetric positive definite slack matrix, an enhanced form of algorithm is introduced. The solution, obtained through linear matrix inequalities and equalities formulation, also unifies the control law design procedure. The obtained results, offering the conditions of PS output controller existence, are illustrated with numerical examples to note effectiveness and applicability of the considered approach.

Quantitative Feedback Design of Linear and Nonlinear Control Systems is a self-contained book dealing with the theory and practice of Quantitative Feedback Theory (QFT). The author presents feedback s

SUMMARY This paper deals with the problem of finite frequency H∞ full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman–Yakubovich–Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H∞ performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.

This paper considers dynamical compensators design for purpose of pole assignment for discrete-time linear periodic systems. Similar to linear time-invariant systems, it is pointed out that the design of a periodic dynamical compensator can be converted into the design of a periodic output feedback controller for an augmented system. Utilizing the recent result on output feedback pole assignment, parametric solutions for this problem are obtained. The design approach can be used as a basis for the robust dynamical compensator design for this type of systems. Combined with a robustness index presented in this paper, robust dynamical compensator design problem is converted into a constrainted optimization problem. A numerical example is employed to illustrate the validity and feasibility of the methods.

In this article, a “Backward in Time Observer” has been designed for linear systems having time delays in output measurements and differences in the sampling rate of input and output measurements. With the proposed observer we are able to recover the performance of the system with no time delay and an equal sampling rate of input and output measurements. Different observers have been designed for time delayed systems by the researcher, but multi-rate time delayed systems have not been discussed so far, hence our proposed observer is able to cater for both of these problems in the system. The proposed observer is simulated for the seeker system of the missile for verification and illustration. Seeker system of missile is a linear time-invariant system having time delay in output measurement. Furthermore, the output measurement through IR camera of the seeker system has a lower sampling rate than its input signal from the gyro.

The role of standard control system structure and that of diophantine or polynomial equations in the computer aided design of linear control systems are investigated. The two tools are shown to lead to simple and efficient algorithms, which provide a uniform design for a variety of control problems and which can be implemented in a highly structured and modular manner.

The paper offers mingling conditions for the interposed H2/H∞ control design for linear discrete-time systems. The goal is to design the feedback control which guarantees bounded H2 performance index and H∞ norm attenuation. Analyzing criteria observances given on a joined H2/H∞ control law, the task is formulated as a feasible problem subject to convex constraints expressed by a system of linear matrix inequalities. The effectiveness and pertinence of the interposed control strategy are demonstrated by results of a numerical example.

The robust H∞ control problem for time-varying uncertain linear systems with time-varying state, and control delays is considered. Based on the Riccati equation approach, we design a robust H∞ linear time-invariant state feedback control law, which stabilizes the system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. A sufficient condition for the existence of the. robust H∞ controller is derived and two synthesis methods are presented for a robust H∞ control law to uncertain time-delay systems. One is to construct a robust H∞ control law by an equivalent linear time-invariant structural description for the sufficient condition and the control law can be obtained by solving an algebraic Riccati equation (ARE). The other method is to transform the sufficient condition into a linear matrix inequality (LMF) problem and the control law can be obtained by solving the LMI. A numerical example is presented to illustrate the obtained results.

The stabilization problem of linear time-varying uncertain delay systems by means of linear constant memoryless state feedback control is investigated here. In the case when uncertain parameters may vary independently in arbitrarily large bounding sets, the locations of uncertain elements in the system parameters play an important role. So far obtained conditions of this problem have been found to have a particular geometric configuration with respect to the permissible locations of uncertain elements. In this paper, such a previously obtained configuration is developed to a basic form of antisymmetric stepwise configuration which is a necessary and sufficient condition for time-varying uncertain systems without delays to be quadratically stabilizable by means of linear constant state feedback control. It is shown that if a given system satisfies such developed conditions then the system is stabilizable via linear constant state feedback control with regardless to the upper bounds of time-varying uncertain parameters and time-varying delays