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.     

Robust control for linear systems with structured state space uncertainty

A recent sufficient condition for the stability robustness of linear systems with time-varying norm bounded state space uncertainty is extended to include the structure of the uncertainty. Our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed-loop eigenvector matrix. Therefore, this robustness result is especially well suited to the design of control systems using eigenstructure assignment. When the uncertainty is time-invariant, our norm is also an upper bound on the incremental eigenvalue perturbations. We also consider the use of Perron weightings to reduce conservatism and the extension of the results to discrete time systems.     

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 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.     

Robust control for linear uncertain systems via linear quadratic state feedback

By the Lyapunov stability criterion and the algebraic Riccati equation, conditions of selecting the weighting matrices in the quadratic cost function are derived so that linear quadratic state feedback can exponentially stabilize a linear uncertain system, provided the uncertainties satisfy the so-called matching conditions and within a given bounding set. Furthermore, two simple but effective algorithms are proposed for systematically selecting the weighting matrices. The main features of this approach are that the uncertain system can be exponentially stabilized with prescribed exponential rate and no precompensator is needed. Two examples are given to illustrate the results.     

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 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.     

时变不确定离散时滞系统的H∞鲁棒控制

研究了一类线性不确定离散时滞系统的H∞鲁棒控制问题,其时变不确定项是范数有界的,但无需满足匹配条件.基于线性矩阵不等式(LMI)方法,得到了可H∞鲁棒镇定的一个充分条件.通过求解一个特定的线性矩阵不等式,即可获得H∞状态反馈控制器.具体算例说明了该方法的有效性.     

滞后广义系统的状态反馈H∞控制

研究了一类状态方程和输出方程均带有时滞的滞后广义系统的H ∞控制问题.利用线性矩阵不等式,首先给出滞后广义系统零解渐近稳定且具有H ∞范数约束的充分条件,进而分别设计无记忆和有记忆状态反馈控制律,保证闭环系统具有上述性能,同时基于线性矩阵不等式的解得到了相应控制器构造方法.最后给出一个数值算例说明文中结论的有效性.     

Robust state feedback control of LTV systems: nonlinear is betterthan linear

Examples of linear control systems with fast time-varying uncertain coefficients are given, which can be stabilized by a nonlinear memoryless state feedback, but cannot be stabilized by a linear time-invariant dynamic state feedback. By means of one of these examples the authors show that the closed loop quadratic stability margin may be infinitely smaller than the actual stability margin     

Global adaptive output feedback control of nonlinear time-delay systems with measurement uncertainty

In this paper,a pair of dynamic high-gain observer and output feedback controller is proposed for nonlinear systems with multiple unknown time delays.By constructing Lyapunov-Krasovskii functionals,it shows that global state asymptotic regulation can be ensured by introducing a single dynamic gain;furthermore,global asymptotic stabilization can be achieved by choosing a sufficiently large static scaling gain when the upper bounds of all system parameters are known.Especially,the output coefficient is allowed to be non-differentiable with unknown upper bound.This paper proposes a generalized Lyapunov matrix inequality based dynamic-gain scaling method,which significantly simplifies the design computational complexity by comparing with the classic backstepping method.     

Global adaptive output feedback control of nonlinear time-delay systems withmeasurement uncertainty

In this paper, a pair of dynamic high-gain observer and output feedback controller is proposed for nonlinear systems withmultiple unknown time delays. By constructing Lyapunov–Krasovskii functionals, it shows that global state asymptoticregulation can be ensured by introducing a single dynamic gain; furthermore, global asymptotic stabilization can be achievedby choosing a sufficiently large static scaling gain when the upper bounds of all system parameters are known. Especially, theoutput coefficient is allowed to be non-differentiable with unknown upper bound. This paper proposes a generalized Lyapunovmatrix inequality based dynamic-gain scaling method, which significantly simplifies the design computational complexity bycomparing with the classic backstepping method.     

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.     

An improved estimate of the robust stability bound of time-delay systems with norm-bounded uncertainty

The robust stability problem of linear time-delay systems with norm-bounded uncertainty is further investigated by using a refined discretized Lyapunov functional approach. A new stability criterion is derived. The computational requirement is reduced for the same discretization mesh. Examples show that the results obtained by this new criterion significantly improve the estimate of the stability limit over some existing results in the literature.     

Decentralized state feedback control of discrete event systems

In this paper, we consider decentralized state feedback control of discrete event systems with a (global) control specification given by a predicate. In this framework, instead of a global state feedback, each local state feedback controls a part of the system according to local information so that global behaviors satisfy the global control specification. We introduce the notion of n-observability of predicates, and present necessary and sufficient conditions for the existence of a decentralized state feedback which achieves the global control specification.     

Robust output feedback stabilizing control for discrete uncertainSISO systems

Given a discrete-time uncertain single-input/single-output (SISO) system, matched uncertainties, and a measured output, a necessary and sufficient condition is given for the existence of a min-max output feedback stabilizing controller. The existence problem of an output stabilizing controller for uncertain systems was treated extensively and solved for the continuous case, but it remained open for the discrete-time case. It turns out that in contrast to the continuous case, the discrete-time system is required to be neither discrete strictly positive real nor even minimum phase and still may satisfy the existence conditions. The paper also contains some new results on discrete positive real functions     

Robust control of robots via linear estimated state feedback

In this note we propose a robust tracking controller for robots that requires only position measurements. The controller consists of two parts: a linear observer part that generates an estimated error state from the error on the joint position and a linear feedback part that utilizes this estimated state. It is shown that this computationally efficient controller yields semi-global uniform ultimate boundedness of the tracking error. An interesting feature of the controller is that it straightforwardly extends results on robust control of robots by linear state feedback to linear estimated-state feedback     

Robust stability for linear time-delay systems with linear parameter perturbations

A new robust state feedback controller design in the time domain is developed for parametrically perturbed linear systems with time delay. The properties of the matrix measure and comparison theorem are employed to investigate the robust stability conditions of systems with linear structured or unstructured perturbations. A method is proposed to design the robust state feedback controller to satisfy the robustness requirement. Examples are given to illustrate the proposed method.     

Delay-dependent H-infinity control for continuous time-delay systems via state feedback

The delay-dependent H-infinity analysis and H-infinity control problems for continuous time-delay systems are studied. By introducing an equality with some free weighting matrices, an improved criterion of delay-dependent stability with H-infinity performance for such systems is presented, and a criterion of existence and some design methods ofdelay-dependent H-infinity controller for such systems are proposed in term of a set of matrix inequalities, which is solved efficiently by an iterative algorithm. Further, the corresponding results for the delay-dependent robust H-infinity analysis and robust H-infinity control problems for continuous time-delay uncertain systems are given. Finally, two numerical examples are given to illustrate the efficiency of the proposed method by comparing with the other existing results.     

Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems.

This paper investigates the problem of designing a fuzzy state feedback controller to stabilize an uncertain fuzzy system with time-varying delay. Based on Lyapunov criterion and Razumikhin theorem, some sufficient conditions are derived under which the parallel-distributed fuzzy control can stabilize the whole uncertain fuzzy time-delay system asymptotically. By Schur complement, these sufficient conditions can be easily transformed into the problem of LMIs. Furthermore, the tolerable bound of the perturbation is also obtained. A practical example based on the continuous stirred tank reactor (CSTR) model is given to illustrate the control design and its effectiveness.