Robust stability of linear systems with delayed perturbations

We consider the robust stability of linear systems with the time-varying perturbations in the time-delayed state, and present sufficient conditions for guaranteeing the asymptotic stability. The obtained results are analytically shown to be less conservative than those reported in the literature. A numerical example is given to show the usefulness of the results     

Robust stability analysis of Smith predictor-based congestion control algorithms for computer networks

Congestion control is a fundamental building block in packet switching networks such as the Internet due to the fact that communication resources are shared. It has been shown that the plant dynamics is essentially made up of an integrator plus time delay and that a proportional controller plus a Smith predictor defines a simple and effective controller. It has also been shown that the TCP congestion control can be modelled using a Smith predictor plus a proportional controller. Due to the importance of this control structure in the field of data network congestion control, we analyse the robust stability of the closed-loop system in the face of delay uncertainties that are present in data networks due to queuing. In particular, by applying a geometric approach, we derive a bound on the proportional controller gain which is necessary and sufficient to guarantee the closed-loop stability for a given bound on the delay uncertainty.     

Robust stability of systems with integral control

A number of necessary and sufficient conditions are derived, which must be satisfied by the plant d.c. gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable. Based on these results, the robustness of integral control systems is analyzed, i.e., the family of plants is defined which are stable when controlled with the same integral controller. Conditions for actuator/sensor failure tolerance of systems with integral control are also given. Finally, parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems.     

Robust stabilization of uncertain impulsive switched systems with delayed control

In this paper, stability criteria and switching controllers’ design problems for uncertain impulsive switched systems with input delay are investigated by using the receding horizon method. Some LMI conditions are derived to guarantee asymptotical stability of an impulsive switched system under a certain designed delayed controller. Finally, a numerical example is presented to illustrate the effectiveness of the results obtained.     

Robust stability analysis of control systems with interval plants

This paper considers the robust stability problem of control systems with interval plants. Under the condition that the controller C(s) stabilizes the nominal plant P0(s) which is the centre of the interval plant, the stability radius of the closed-loop system is characterized in terms of the eigenvalues of some frequency-independent Hurwitz-like matrices.     

时滞不确定采样控制系统的鲁棒稳定性

本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.     

Robust finite time stability of fractional-order linear delayed systems with nonlinear perturbations

This letter is concerned with robust stability of fractional-order linear delayed system with nonlinear perturbations over finite time interval. By using inequality technique, two new sufficient conditions for the finite time stability for such systems with order α: 0 α ≤ 0.5 and 0.5 < α < 1 are presented, respectively. A numerical example is presented to demonstrate the validity and feasibility of the obtained results.     

Robust stability analysis of robot control systems

Some robust stability measures for state-space models are discussed. These measures are used for assessing the robustness of a robotic system controlled by a form of the PID control algorithm. The highly nonlinear and strongly coupled robot model is replaced by a nominal linear model involving modelling uncertainty. The amount of uncertainty under which the robotic system can maintain its stability and tracking performance is determined using the above measures. The parametric sensitivity of the robotic system is also briefly considered.     

Robust stability of uncertain impulsive control systems with time-varying delay

In this paper, we are concerned with the robust stability problem of an uncertain impulsive control system with time-varying delay. By employing the formula for the variation of parameters and estimating the Cauchy matrix, several criteria on robust exponential stability are derived and the exponential convergence rate is estimated. Based on $P$-norm and $P$-measure of matrix, it is seen that our sufficient conditions are less restrictive than the ones in the earlier publication. Some numerical examples and simulations are given to illustrate the theoretical results and to show that the criteria can be applied to stabilize the unstable continuous system with time delays and uncertainties by utilizing impulsive control.     

Robust stability of reset control systems with uncertain output matrix

The main difficulty in stability analysis of reset control systems comes from their state-dependent reset mechanism. It becomes more challenging when output matrix suffers from uncertainties which make the reset time instants uncertain. In this paper, existing quadratic stability results for uncertainty-free reset systems are extended to the case with uncertainty in the output matrix. By constructing special parameter-dependent full rank annihilators of the output matrix, it is proved that the dissipativeness of reset action is equivalent to the feasibility of an LMI plus some structural constraints on the Lyapunov matrix. For the time-varying uncertainty case, necessary and sufficient conditions for quadratic stability are obtained. For the constant uncertainty case, a sufficient condition for affine quadratic stability is also obtained. All the results are given in terms of LMIs which can be efficiently verified.     

Robust absolute stability of Lurie interval control systems

This paper considers robust absolute stability of Lurie control systems. Particular attention is given to the systems with parameters having uncertain, but bounded values. Such so‐called Lurie interval control systems have wide applications in practice. In this paper, a number of sufficient and necessary conditions are derived by using the theories of Hurwitz matrix, M matrix and partial variable absolute stability. Moreover, several algebraic sufficient and necessary conditions are provided for the robust absolute stability of Lurie interval control systems. These algebraic conditions are easy to be verified and convenient to be used in applications. Three mathematical examples and a practical engineering problem are presented to show the applicability of theoretical results. Numerical simulation results are also given to verify the analytical predictions. Copyright © 2007 John Wiley & Sons, Ltd.     

Robust backstepping control for a class of time delayed systems

In this note, the problem of robust output feedback control for a class of nonlinear time delayed systems is considered. The systems considered are in strict-feedback form. State observer is first designed, then based on the observed states the controller is designed via backstepping method. Both the designed observer and controller are independent of the time delays. Based on Lyapunov stability theory, we prove that the constructed controller can render the closed-loop system asymptotically stable. Simulation results further verify the effectiveness of the proposed approach.     

Robust tuning of a generalized predictor-based controller for integrating and unstable systems with long time-delay

In this work, a general structure to control long time-delay plants is proposed and an easy methodology to tune the control parameters is outlined. All the sensitivity transfer functions are delay free. The proposed scheme is equivalent to the Smith predictor but able to cope with any kind of systems, including non-minimum phase, unstable and integrating plants. The controllers are designed based on the delay free model. Contrary to other approaches, other than for the digital implementation, no delay approximation is used. A tuning parameter is provided in order to reach an intuitive tradeoff between performance and robust stability. A comparative analysis with respect to recently successful proposals shows a substantial improvement in the performance/robustness tradeoff as well as in the tuning process.     

Robust stability bounds for multi-delay networked control systems

In this paper, the robust stability of a perturbed linear continuous-time system is examined when controlled using a sampled-data networked control system (NCS) framework. Three new robust stability bounds on the time-invariant perturbations to the original continuous-time plant matrix are presented guaranteeing stability for the corresponding discrete closed-loop augmented delay-free system (ADFS) with multiple time-varying sensor and actuator delays. The bounds are differentiated from previous work by accounting for the sampled-data nature of the NCS and for separate communication delays for each sensor and actuator, not a single delay. Therefore, this paper expands the knowledge base in multiple inputs multiple outputs (MIMO) sampled-data time delay systems. Bounds are presented for unstructured, semi-structured, and structured perturbations.     

Improved disturbance rejection for predictor-based control of MIMO linear systems with input delay

In this paper, we are concerned with the predictor-based control of multi-input multi-output (MIMO) linear systems with input delay and disturbances. By taking the future values of disturbances into consideration, a new improved predictive scheme is proposed. Compared with the existing predictive schemes, our proposed predictive scheme can achieve a finite-time exact state prediction for some smooth disturbances including the constant disturbances, and a better disturbance attenuation can also be achieved for a large class of other time-varying disturbances. The attenuation of mismatched disturbances for second-order linear systems with input delay is also investigated by using our proposed predictor-based controller.     

Robust stability functionals of state delayed systems with polytopic type uncertainties via parameterdependent Lyapunov functions

This paper considers the problem of robust stability for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. Both delay-independent and delay-dependent stability conditions are characterized by linear matrix inequalities which allow the use of parameter-dependent Lyapunov functionals to analyse the system stability against parameter perturbations, and therefore improve the conservativeness resulting from the single Lyapunov functional. In order to determine the maximum of time-delay within which the system remains stable, the problem can be cast into a generalized eigenvalue problem and solved by standard LMI solvers. Two examples are included to illustrate the proposed method.     

Robust stability of feedback control systems with uncertain parameters and unmodeled dynamics

Recent results on a generalization of Kharitonov’s interval polynomial problem allow linearly dependent perturbations in the coefficients of a polynomial, and the main objective is to provide computationally tractable criteria for robust stability. In this paper robust-stability criteria are provided in an even more general setting—one which also accommodates unmodeled dynamics. In addition, the test given for robust stability totally avoids so-called “edge combinatorics,” greatly facilitating numerical computation. This research was supported by the National Science Foundation under Grants ECS-8612948 and ECS-8451519 and in part by AFOSR Grant 880020, Honeywell and GE.     

Robust stability and control of uncertain linear discrete-time periodic systems with time-delay

This paper deals with the problems of robust stability analysis and robust control of linear discrete-time periodic systems with a delayed state and subject to polytopic-type parameter uncertainty in the state-space matrices. A robust stability criterion independent of the time-delay length as well as a delay-dependent criterion is proposed, where the former applies to the case of a constant time-delay and the latter allows for a time-varying delay lying in a given interval. The developed robust stability criteria are based on affinely uncertainty-dependent Lyapunov–Krasovskii functionals and are given in terms of linear matrix inequalities. These stability conditions are then applied to solve the problems of robust stabilization and robust _H∞$H_{\infty }$  control via static periodic state feedback. Numerical examples illustrate the potentials of the proposed robust stability and control methods.     

Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals

This paper considers the problem of robust stability and robust stabilization for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. First of all, for robust stability problem, we exploit new matrix inequalities characterization of delay-dependent quadratic stability results, demonstrate that it allows the use of parameter-dependent Lyapunov functionals, and develop control design methods based on linear matrix inequalities (LMIs) for solving the robust control problem. Next, the problem of determining the maximum time-delay under which the system remains stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. Finally, illustrative examples are given to demonstrate the advantage of these new representations.