Robust analysis and synthesis of linear time-delay systems with norm-bounded time-varying uncertainty

The problems of robust analysis and synthesis of systems with state-delay and norm-bounded time-varying parameter uncertainty are studied. It is shown that these problems are equivalent to the H_∞ analysis and synthesis problems of an auxiliary system, which is independent of the time-delay and the uncertainty in the system. The necessary and sufficient conditions for the equivalence are developed. Thus any standard H_∞ analysis and synthesis method can be used to solve this problem.     

Local stabilization for linear discrete-time systems with bounded controls and norm-bounded time-varying uncertainty

The problem of the local stabilization of linear discrete-time systems subject to bounded controls and suffering from uncertainty of the norm-bounded time-varying type is addressed. From the solution of a certain discrete Riccati equation, a control gain and a set of safe initial conditions are obtained. The asymptotic stability of the saturated closed-loop system is then locally guaranteed for all admissible uncertainties. It is also shown how the control problem can be translated into L.M.I. conditions. The connections between local stability results and disturbance rejection problem are investigated. In the presence of control saturation, it is thus shown that it is possible to reject a certain class of perturbations. Finally, a discretized model of the inverted pendulum allows us to illustrate the results. © 1998 John Wiley & Sons, Ltd.     

Robust H∞ control for linear discrete-time systems with norm-bounded time-varying uncertainty

The problem of robust H_∞ analysis and synthesis for linear discrete-time systems with norm-bounded time-varying uncertainty is studied in this paper. It will be shown that this problem is equivalent to the problem of H_∞ analysis and synthesis of an auxiliary system. The necessary and sufficient conditions for the equivalency are proved. Thus the original problem can be solved by existing H_∞ control methods.     

The robustness of controllability and observability for discrete linear time-varying systems with norm-bounded uncertainty

Controllability and observability of discrete linear time-varying systems with norm-bounded parameter uncertainties are analyzed in this note. Like in the continuous case, we propose the sufficient conditions, which ensure controllability and observability of the uncertain system. The proposed conditions allow the evaluation of controllability and observability of the uncertain system without knowledge of specific values of uncertainties.     

Robust memoryless H∞ controller design for linear time-delay systems with norm-bounded time-varying uncertainty

We consider the robust H_∞ control problem for linear time-delay systems with norm-bounded time-varying uncertainty. Based on the Riccati-equation approach, we present a method for designing a robust memoryless 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.     

Robust stabilization of linear discrete-time systems with time-varying input delay

This paper presents a sufficient condition to stabilize linear discrete-time systems with time-varying input delay and model uncertainties. The key idea consists of applying Artstein’s reduction method and the scaled bounded real lemma; the robust stabilization problem is cast as a set of linear matrix inequalities on a transformed delay-free system. Hence, a novel convex characterization of the problem, an alternative to bilinear matrix inequalities in prior literature, is provided. Predictor-based controllers and robust state-feedback stabilization are particular cases of the proposal. Furthermore, numerical examples show that this proposal may improve tolerance against delay variations when compared to other methods available in literature.     

Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty

This paper studies, via a linear matrix inequality approach, the problem of Hinfinity control for discrete time-delay linear systems with parametric uncertainty. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and time delay in the state. First, the problem of robust stability of the underlying system is investigated. Next, we address the problem of robust Hinfinity state feedback control in which both robust stability and a prescribed Hinfinity performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a linear matrix inequality has a symmetric positive definite solution.     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.     

线性时变系统的一种鲁棒镇定控制器设计方法

针对一类线性时变系统提出一种状态反馈镇定控制器设计方法,该反馈控制器能将线性时变系统转化为一个稳定的定常闭环系统.借助线性系统的特征结构配置参数化方法,得到含待求参数的控制器解析形式,并给出控制器的可解性判据.在满足可解性的基础上,进一步对控制器进行了多目标优化设计,使其在保证系统稳定性的同时,具有良好的鲁棒性和干扰抑制能力.通过一个时变卫星姿态控制系统的实际设计表明了该方法的有效性.     

Quadratic stabilization of continuous time systems with state-delayand norm-bounded time-varying uncertainties

This paper develops a method for designing a feedback control law to stabilize a class of uncertain linear systems. The class of systems under consideration is described by a continuous-time model with variable-state delay and depends on time-varying unknown-but-bounded uncertain parameters. It is shown that the construction of the stabilizing controller involves solving a certain algebraic Riccati equation. Several previous results are derived as interesting special cases. Finally, a simulation example is presented to illustrate the analytical developments     

On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty

This paper investigates the robust stability of uncertain linear neutral systems with time-varying discrete delay. A delay-dependent stability criterion is obtained and formulated in the form of a linear matrix inequality. Two numerical examples are given to indicate significant improvements over some existing results.     

Robust constrained predictive control of uncertain norm-bounded linear systems

A novel robust predictive control algorithm is presented for uncertain discrete-time input-saturated linear systems described by structured norm-bounded model uncertainties. The solution is based on the minimization, at each time instant, of a semi-definite convex optimization problem subject to a number of LMI feasibility constraints which grows up only linearly with the control horizon length N. The general case of arbitrary N is considered. Closed-loop stability and feasibility retention over the time are proved and comparisons with robust multi-model (polytopic) MPC algorithms are reported.     

Quadratic stability and stabilization of linear systems withFrobenius norm-bounded uncertainties

In this paper, a quadratic stability condition and a quadratic stabilizer are proposed for linear systems with Frobenius norm-bounded uncertainties. The necessary and sufficient condition for the quadratic stability of the uncertain system is given by a Riccati inequality. The proposed state feedback quadratic stabilizer can be obtained by solving a Riccati equation     

Robust stabilization for generalized state-space systems with uncertainty

This paper is concerned with the problem of robust stabilization for generalized state-space systems with parameter uncertainty. The parameter uncertainty under consideration is time-invariant and unknown, but is norm-bounded. The problem we address is to design a state feedback controller such that the resulting closed-loop system is regular, impulsefree and stable for all admissible uncertainties. Via the notion of 'stabilizability and impulse eliminatibility' the robust stabilization problem is solved. Necessary and sufficient conditions for stabilizability and impulse eliminatibility are derived. When these conditions are satisfied, the desired stabilization state feedback controller can be constructed through finding parameters satisfying a certain matrix equation. Finally, an illustrative example is given to show the feasibility of the proposed technique.     

Robust stabilization for systems with rank-one uncertainty structure

This paper solves a class of robust control problems, with output feedback, for systems with mixed parametric uncertainty and unmodeled dynamics. This class of problems is characterized by a special rank-one assumption on the transfer matrix of the nominal plant. Under this assumption, the robust stabilization problem is reduced to a convex feasibility problem involving linear matrix inequalities. The data necessary to assemble these inequalities can be readily obtained from a state-space model of the nominal plant.     

Lyapunov-stable adaptive stabilization of non-linear time-varying systems with matched uncertainty

This paper considers direct adaptive stabilization of multi-input non-linear time-varying systems with full-state feedback and state-and-time-dependent uncertainty. The novel result of this paper is a single-parameter adaptive controller that yields a Lyapunov-stable closed-loop system. We demonstrate the controller on a non-linear spring-mass-damper, a three-degree-of-freedom Mathieu equation, and a 4th-order non-linear time-varying system.     

On stabilization for discrete linear time-varying systems

In this paper, we consider the stabilization problem for discrete linear time-varying systems in an operator-theoretic framework. By using the complete finiteness of a certain discrete nest algebra, we show that a system is stabilizable if and only if it has one kind of strong representation and we also give a parametrization for all the stabilizing controllers in terms of this strong representation. This result extends the Youla parametrization theorem by only requiring a strong left or a strong right representation but not both. The strong stabilization problem is also discussed.     

On strong stabilization for linear time-varying systems

This paper deals with the strong stabilization problem for linear time-varying systems and gives a sufficient condition, in terms of the coprime factors, for the existence of strong stabilizers for such a system.     

Robust stabilization of linear time-invariant systems

The problem of robustly stabilizing families of linear time-variant plants consisting of a nominal plant and its frequency domain neighborhood is discussed. Necessary and sufficient conditions are obtained for robust stabilizability of such families of plants. The set of robustly stabilizing controllers is parameterized and the largest achievable stability margin is characterized for a linear time-invariant plant