Observer-based robust stabilization for uncertain systems with unknown time-varying delay

This paper focuses on the problem of robust stabilization for a class of linear systems with uncertain parameters and time varying delays in states. The parameter uncertainty is continuous, time varying, and norm-bounded. The state delay is unknown and time varying. The states of the system are not all measurable and an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are dependent on the size of time delay and on the size of delay derivative. Finally, an example is given to illustrate the effectiveness of the proposed control method.     

On robust stabilization of Markovian jump systems with uncertain switching probabilities

This brief paper is concerned with the robust stabilization problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertain Markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix. First, a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities. Then, a sufficient condition is proposed for the design of robust state-feedback controllers. A globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively. Finally, a numerical simulation is used to illustrate the developed theory.     

一类含有输入时滞的不确定切换系统的鲁棒指数镇定

针对一类含有输入时滞的不确定切换系统,讨论了鲁棒指数镇定问题,提出了可行的切换控制器和切换信号的设计方法．首先,运用还原法将具有时滞的切换系统转化为无时滞的切换系统;然后,基于线性矩阵不等式,给出了系统在切换控制器和切换信号作用下鲁棒指数可镇定的充分条件,并利用多Ｌｙａｐｕｎｏｖ函数方法给出了定理的详细证明;最后,利用数值仿真例子验证了该方法的有效性．     

Robust stabilization of uncertain systems with unknown input delay

This paper is concerned with the robust controller design for uncertain input-delayed systems. The time delay is assumed to be an unknown constant. A controller with delay feedback for the robust stabilization of the system is proposed. The stability criterion of the closed-loop system is derived in terms of linear matrix inequalities (LMIs). Examples show that in many cases our method can give less conservative results than those by the existing methods. Moreover, for the same cases, our controllers have lower feedback gains than the existing ones.     

Adaptive robust control of uncertain time delay systems

The problem of adaptive robust control for uncertain linear systems with multiple delays occurring in the state variables is studied in this paper. The essential requirement for the uncertainties is that they satisfy matching conditions and are norm-bounded, but the bounds of the uncertainties are not necessarily known. An adaptive controller is developed based on linear matrix inequality technique and it is shown that the controller can guarantee the state variables of the closed loop system to converge, globally, uniformly and exponentially, to a ball in the state space with any pre-specified convergence rate. The effectiveness of our approach has been verified by its application in the control of river pollution process for the purpose of preserving standards of water constituents in streams.     

一类输入受限不确定时滞系统的准Min-Max模型预测控制

针对一类输入受限离散不确定时滞系统,提出一种基于准Ｍｉｎ-Ｍａｘ的模型预测控制器设计方法．定义了时滞系统的鲁棒性能指标,给出了系统稳定的充分条件,通过求解ＬＭＩ凸优化获得控制器．准Ｍｉｎ-Ｍａｘ预测控制将当前控制量作为独立优化变量,与其他作为反馈控制的时域控制序列分开处理,有效地降低了算法的保守性,提高了可行性．仿真算例验证了所提出控制方法的有效性．     

Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers

The problems of robust stability and robust stabilization of uncertain linear systems with distributed delay occurring in the state variables are studied in this paper. The essential requirement for the uncertainties is that they are norm-bounded with known bounds. Conditions for the robust stability of distributed time delay systems are given and a design method for the robust stabilizing control law of the uncertain systems is presented. The proposed method is applied to the stabilization of combustion in the chamber of a liquid monopropellant rocket motor. It is found that the combustion can be robustly stabilized when the two parameters pressure exponent γ and maximal time lag r vary in specified intervals, respectively.     

Robust stabilization of Markovian delay systems with delay-dependent exponential estimates

A sufficient condition for the exponential estimates of a class of Markovian systems with time delay is established for the first time in terms of the linear matrix inequality (LMI) technique. The estimating procedure is implemented by solving an LMI. The proposed condition is also extended to the uncertain case. Moreover, a state feedback stabilizing controller which makes the closed-loop system exponentially stable with a prescribed lower bound of decay rate is designed. Numerical examples are provided to illustrate the effectiveness of the theoretical results.     

Delay‐dependent robust stabilization for uncertain stochastic switching systems with distributed delays

This paper deals with the problem of robust stabilization for a class of uncertain stochastic switching systems with distributed delays. The purpose is to design a memory controller, which guarantees that the resulting closed‐loop system is mean‐square asymptotically stable. In terms of a set of linear matrix inequalities, a delay‐dependent condition is proposed and a robust memory controller is designed. Two numerical examples are provided to illustrate the effectiveness of the proposed method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust stabilization of uncertain time-varying discrete systems and comments on “an improved approach for constrained robust model predictive control”

This paper addresses the robust stabilizability problem of linear discrete-time systems with time-varying polytopic uncertainties. A state feedback control law is proposed based on the construction of a parameter-dependent Lyapunov function. Also, it points out that the main results of Cuzzola, Geromel, and Morari (Automatica 38 (2002) 1183-1189) are incorrect and presents the corrected version of these results.     

Delay-dependent stabilization of linear systems with time-varying state and input delays

The integral-inequality method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: . In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither (A,B₁) nor (A+A₁,B₁) is stabilizable.     

A new design of robust filters for uncertain systems

In this paper, a structured polynomial parameter-dependent approach is proposed for robust H₂ filtering of linear uncertain systems. Given a stable system with parameter uncertainties residing in a polytope with s vertices, the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain. A new polynomial parameter-dependent idea is introduced to solve the robust H₂ filtering problem, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain, or the linearly parameter-dependent framework that uses linear convex combinations of s matrices. This idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices. Linear matrix inequality (LMI) conditions are obtained for the existence of admissible filters and based on these, the filter design is cast into a convex optimization problem, which can be readily solved via standard numerical software. Both continuous and discrete-time cases are considered. The merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods, as shown both theoretically and through extensive numerical examples.     

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network-induced delay

This paper addresses the state derivative feedback control problem for uncertain polytopic systems subject to an uncertain sampling period and network-induced delay. The distinctive contribution relies on the direct design of a robust state derivative feedback controller employing an augmented discretized model derived in terms of the state derivative feedback such that network-induced delay and uncertain sampling periods can be incorporated from the original continuous-time state-space representation into the discretized model. Two augmented models are provided to handle longer input time delays, as well as delays less or equal to the sampling period. In this work, all the uncertain parameters are modeled as a polytopic form whose resulting discrete-time model has matrices with polynomial dependence on the uncertain parameters and an additive norm-bounded term featuring the discretization residual error. Moreover, synthesis conditions are derived using a set of linear matrix inequalities (LMI) to solve the stabilization problem for this class of systems under different input time delays. Finally, numerical simulations are carried out to evaluate the effectiveness of the proposed method.     

Adaptive control for a class of nonlinear systems with time-varying delays in state and input

This paper is concerned with the adaptive stabilization problem of uncertain input delayed systems.A solution to this problem is given for a class of uncertain nonlinear systems with time-varying delays in both state and input.An adaptive asymptotically stabilizing controller,which can guarantee the stability of the closed-loop system and the convergence of the original system state,is designed by means of the Lyapunov-Krasovskii functional stability theory combined with linear matrix inequalities (LMIs) an...     

Adaptive backstepping control of uncertain systems with unknown input time-delay

In this paper, we establish the robustness of adaptive controllers designed using the standard backstepping technique with respect to unmodeled dynamics involving unknown input time delay. While noting that some results on robust stabilization of non-minimum phase systems using the backstepping technique are available, we realize that the standard adaptive backstepping technique has only been shown applicable to unknown minimum phase systems. Another significance of our result is to enable the class of systems stablizable by adaptive backstepping controllers to cross the boundary of minimum phase systems, since systems with input time delay belong to non-minimum phase systems. Moreover, the L₂ and L_∞ norms of the system output are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters.     

Delay-dependent robust H-infinity filtering for uncertain linear systems with time-varying interval delay

This paper proposed a design method for delay-dependent robust H-infinity filter of linear systems with uncertainty and time-varying interval delay.The proposed method was shown to be much simpler than existing ones while giving significant improvement to the existing results.The key step in the method was to construct a special type of Lyapunov functional for the filter design problem.Unlike the existing techniques,the proposed method employed neither free weighting matrices nor any model transformation,le...     

An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties.A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix.Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases.A numerical example illustrates the improvement over the existing ones.     

An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.     

An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.     

Delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays

This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality （LMI） approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed- loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods.