Design of Norm-Bounded and Sector-Bounded LQG Controllers for Uncertain Systems

The design of linear-quadratic-Gaussian (LQG) controllers is addressed for uncertain linear time-invariant systems that are either norm bounded or belong to a given sector. The system matrices are assumed to be affine functions of parameters confined to a convex polytopic region in the parameter space. Methods are developed for designing controllers which satisfy certain norm or sector conditions and are simultaneously optimal in the LQG sense. The resulting controllers provide robust stability as well as optimal performance.     

一类不确定线性切换系统二次鲁棒稳定性的充分条件

本文研究了一类不确定线性切换系统的二次鲁棒稳定性问题.首先利用矩阵集的严格完备性设计切换律,导出了二次鲁棒稳定的充分条件.同时得到了在任意切换策略下,当矩阵集的所有矩阵为负定时保证切换系统二次鲁棒稳定性.在适当的假设下,这些条件可以表示为矩阵不等式.最后,用数值例子对所得结果加以阐明,说明了文中结果的正确性.     

Stability analysis and uniform ultimate boundedness control synthesis for a class of nonlinear switched difference systems

In this paper, we deal with stability analysis of a class of nonlinear switched discrete-time systems. Systems of the class appear in numerical simulation of continuous-time switched systems. Some linear matrix inequality type stability conditions, based on the common Lyapunov function approach, are obtained. It is shown that under these conditions the system remains stable for any switching law. The obtained results are applied to the analysis of dynamics of a discrete-time switched population model. Finally, a continuous state feedback control is proposed that guarantees the uniform ultimate boundedness of switched systems with uncertain nonlinearity and parameters.     

一般Lurie型控制系统的鲁棒绝对稳定性

本文得到一般的Ｌｕｒｉｅ类型非线性控制系统的鲁棒绝对稳定性的充分条件;同时,给出一些例子说明本文结果的有效性．     

Stability Analysis of Optimal Control Systems via Liapunov Method

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Lurie不确定间接控制系统的鲁棒绝对稳定性

利用Razumikhin技术和向量不等式方法,通过构造适当的Lyapunov函数,对具有多个时变时滞lurie不确定间接控制系统的鲁棒绝对稳定性的问题进行了研究,给出了该系统时滞相关鲁棒稳定的充分条件.其结论与已有文献结果进行比较,说明所得结果推广了已有文献的结果,具有更好的实用性.最后给出一个例子说明本文结果.     

Robust Stabilization of Linear Systems with Delayed State and Control

Robust stabilization of linear systems with delays on both the state and control input is studied in this paper. Using an improved Lyapunov-Krasovskii functional, we establish new criteria that ensure the robust stability of the closed-loop system with memoryless state feedback controls. The generalized conditions are derived in terms of linear matrix inequalities (LMIs), allowing us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution and can be easily solved by numerical algorithms. This work was supported by the National Basic Program in Natural Sciences. The authors thank the anonymous referees for valuable comments to improve the paper.     

Delay Range-Dependent Stability Analysis for Markovian Jumping Stochastic Systems with Nonlinear Perturbations

This article addresses the problem of delay-dependent stability for Markovian jumping stochastic systems with interval time-varying delays and nonlinear perturbations. The delay is assumed to be time-varying and belongs to a given interval. By resorting to Lyapunov–Krasovskii functionals and stochastic stability theory, a new delay interval-dependent stability criterion for the system is obtained. It is shown that the addressed problem can be solved if a set of linear matrix inequalities (LMIs) are feasible. Finally, a numerical example is employed to illustrate the effectiveness and less conservativeness of the developed techniques.     

Exponential Stability for Time-Delay Systems with Interval Time-Varying Delays and Nonlinear Perturbations

In this paper, the problem of an exponential stability for time-delay systems with interval time-varying delays and nonlinear perturbations is investigated. Based on the Lyapunov method, a new delay-dependent criterion for exponential stability is established in terms of LMI (linear matrix inequalities). Numerical examples are carried out to support the effectiveness of our results.     

一类不确定时变时滞系统的鲁棒自适应稳定控制

研究了一类不确定时变时滞系统的鲁棒自适应稳定控制问题.系统包含多变时滞非线性扰动.基于Lyapunov稳定性理论和Lyapunov-K rasovsk ii型泛函设计出了一种无记忆的自适应状态反馈控制器,并证明了满足一定条件时,此控制器使得闭环系统最终一致有界.     

Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems

Second-order sufficient optimality conditions (SSC) are derived for an optimal control problem subject to mixed control-state and pure state constraints of order one. The proof is based on a Hamilton-Jacobi inequality and it exploits the regularity of the control function as well as the associated Lagrange multipliers. The obtained SSC involve the strict Legendre-Clebsch condition and the solvability of an auxiliary Riccati equation. They are weakened by taking into account the strongly active constraints.     

Sufficient Optimality Conditions for Optimal Control Problems with State Constraints

It is well-known in optimal control theory that the maximum principle, in general, furnishes only necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum principle turns to be likewise a sufficient condition. Here an invexity type condition for state constrained optimal control problems is defined and shown to be a sufficient optimality condition. Further, it is demonstrated that all optimal control problems where all extremal processes are optimal necessarily obey this invexity condition. Thus optimal control problems which satisfy such a condition constitute the most general class of problems where the maximum principle becomes automatically a set of sufficient optimality conditions.     

具有时变灰参数的随机时滞系统的p-阶矩指数鲁棒稳定性

利用灰矩阵的矩阵覆盖集的分解技术和Lyapunov函数法,研究了具有时变灰色参数的随机时滞系统的p-阶矩指数鲁棒稳定性问题,得到了该系统p-阶矩指数鲁棒稳定的时滞独立和时滞依赖的条件,并通过数值例子说明了判别条件的有效性和实用性.     

Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties

In this paper, the problem of the robust stabilization for a class of uncertain linear systems with multiple time-varying delays is investigated. The uncertainty is nonlinear time-varying and does not require a matching condition. A memoryless state-feedback controller for the robust stabilization of the system is proposed. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, two sufficient conditions for the stability are derived. Two numerical examples are given to illustrate the proposed method.     

中立型时滞系统的时滞相关鲁棒控制

研究了一类具有时变时滞中立型系统的时滞相关鲁棒控制问题.利用Lyapunov-K rasovsk ii泛函方法,借助于积分不等式,得到了系统经无记忆状态反馈控制后可镇定的时滞相关条件.最后给出数值例子验证了所得结果的有效性.     

Decentralized Adaptive Robust Tracking and Model Following for Large-Scale Systems Including Delayed State Perturbations in the Interconnections

The problem of decentralized robust tracking and model following is considered for a class of uncertain large-scale systems including delayed state perturbations in the interconnections. In this paper, it is assumed that the upper bounds of the delayed state perturbations, uncertainties, and external disturbances are unknown. A modified adaptation law with σ-modification is introduced to estimate such unknown bounds, and on the basis of the updated values of these unknown bounds, a class of decentralized local memoryless state feedback controllers is constructed for robust tracking of dynamical signals. The proposed decentralized adaptive robust tracking controllers can guarantee that the tracking errors between each time-delay subsystem and the corresponding local reference model without time-delay decrease uniformly asymptotically to zero. Finally, a numerical example is given to demonstrate the validity of the results.     

Robust Stability and Stabilizability of Markov Jump Linear Uncertain Systems with Mode-Dependent Time Delays

This paper studies the class of uncertain linear systems with time delay and Markov jump disturbance, in which the time delay is assumed to be dependent on the system mode. An LMI-based condition for this class of systems to be robustly stable is established. Sufficient conditions for the robust stabilizability under a state feedback controller are developed, and an LMI-based method to design the state feedback is proposed. Numerical examples are worked out to show the usefulness of the theoretical results.     

几类Lurie型控制系统绝对稳定性充分必要条件

本借助部分变元绝对稳定性的充要条件，得出几类Lurie型控制系统绝对稳定性充分必要条件，这些判据为显式的代数形式，易于验证，也便于在实践中应用。     

Approximate Optimal Control and Stability of Nonlinear Finite- and Infinite-Dimensional Systems

We consider first nonlinear systems of the formx=A(x)x+B(x)u together with a standard quadratic cost functional and replace the system by a sequence of time-varying approximations for which the optimal control problem can be solved explicitly. We then show that the sequence converges. Although it may not converge to a global optimal control of the nonlinear system, we also consider a similar approximation sequence for the equation given by the necessary conditions of the maximum principle and we shall see that the first method gives solutions very close to the optimal solution in many cases. We shall also extend the results to parabolic PDEs which can be written in the above form on some Hilbert space.     

Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time

We give spectral and algebraic coefficient criteria (necessary and sufficient conditions) as well as sufficient algebraic coefficient conditions for the Lyapunov asymptotic stability of solutions to systems of linear deterministic or stochastic delay difference equations with continuous time under white noise coefficient perturbations for the case in which all delay ratios are rational. For stochastic systems, mean-square asymptotic stability is studied. The Lyapunov function method is used. Our criteria on algebraic coefficients and our sufficient conditions are stated in terms of matrix Lyapunov equations (for deterministic systems) and matrix Sylvester equations (for stochastic systems).