Vertex results for the steady state analysis of uncertain systems

It is shown that, if a system is robustly stable and if the dependence on the uncertain parameters is to an extent multiaffine, then the extreme values of the steady-state response over the entire set of parameters is equal to the extreme values over just the vertices of the parameter set. This vertex result is doubly useful because it is valid in both continuous time and discrete time     

New results for the stability of uncertain time-delay systems

In this paper, based on the Lyapunov stability theorem associated with matrix measure techniques, some new delay-independent criteria for asymptotic stability of linear perturbed time-delay systems are proposed. Furthermore, the stability degree testing problem of the above systems is also investigated. From the given examples, we demonstrate the superiority of these quantitative results by comparing them with other approaches presented in the literature     

Further results on the robust stability of uncertain time-delay systems

We present new several sufficient conditions for the robust stability of uncertain time-delay systems. These conditions represent the delay-independent asymptotic stability and the decaying rate for uncertain single time-delay systems. These results are then extended to uncertain composite linear systems with time delays. The superiority of these results is demonstrated by comparing them to those given by Wang et al. (1987).     

不确定系统的鲁棒稳定性

针对一类不确定非线性系统,基于王立新1994年提出的监督控制方案提出了一种SISO系统的模型参考自适应模糊控制器设计的新方案.该方案同时利用广义多线性模糊逻辑系统的逼近能力和I型模糊逻辑系统的逼近能力,不仅能保证闭环系统状态全局稳定,而且有效避免了控制增益可能出现的奇异性问题.理论分析证明了跟踪误差收敛到零,仿真结果表明了该方法的有效性.     

Further results on global practical tracking via adaptive output feedback for uncertain nonlinear systems

This paper is concerned with the global practical tracking via adaptive output feedback for a class of uncertain nonlinear systems. The system under investigation possesses function control coefficients, the polynomial-of-output growth rate and serious unknowns in the system nonlinearities and the reference signal, and hence is essentially different from those in the closely related literature. To solve the problem, a high-gain observer is introduced to reconstruct the unmeasured system states. The involved high gain is the multiplication of two dynamic gains: one is to compensate the polynomial-of-output in the system growth rate, and the other one is to overcome the serious unknowns in the system and reference signal and the extra system nonlinearities in function control coefficients. Based on the high-gain observer, an adaptive output-feedback controller is successfully designed to guarantee that, for any initial condition of the system, all signals of the closed-loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical example demonstrates the effectiveness of the proposed method.     

Robust Kalman filtering for uncertain systems

This paper studies the problem of Kalman filter design for uncertain systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainties in both the state and measurement matrices. The problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties. A Riccati equation approach is proposed to solve the above problem. Furthermore, a suboptimal covariance upper bound can be computed by a convex optimization.     

Destabilizing strategies for uncertain linear systems

The paper the problem of determining destabilizing strategies for uncertain linear systems was researched. Sufficient conditions for the existence of a destabilizing strategy were presented and an algorithm for computation of the destabilizing strategy was given. The approach elaborated in the paper develops some of the previous results which did not provide methods for calculation of destabilizing switching     

Quadratic stabilization for uncertain stochastic systems

1IntroductionInthelast decades ,manyauthors studiedrobust quadraticstabilization control of deterministic linear systems withparameter uncertainty or structured uncertainty, see[1 ~8] . Robust quadratic stability and stabilization ofdeterministic systems were first introduced by [1] ,bymeans of a common Lyapunovfunction.Most earlier resultson robust quadratic stabilization,including some necessaryand sufficient conditions , were expressed in terms ofRiccati_type equations or inequalities , wh…     

Structure invariance for uncertain nonlinear systems

A unified study of three control problems associated to multi-input multi-output nonlinear systems with uncertainties is presented, namely, input-state linearization by static state feedback, input-output decoupling by static state feedback and input-output decoupling by dynamic compensation. For each of these problems, geometric conditions which describe intrinsic structural invariance properties are given     

Stochastic models for uncertain flexible systems

If a spectral operator is perturbed by an infinite-dimensional white noise process, it generates a stochastic evolution operator which has well defined second order properties. This type of stochastic bilinear spectral evolution equation may be used to model uncertainty of the higher modes in flexible systems. Three typical examples of flexible beams with bilinear white noise perturbations are analysed in detail and conditions are given for the existence of a steady state covariance operator.     

Sampled-data controller design for uncertain systems

Presents a sampled-data controller design methodology for uncertain systems. A continuous system with bounded time-varying uncertainty is sampled at intervals of length T. The controller is designed using a Riccati equation approach by neglecting O(T²) uncertainty terms in the discretized system. Stability is verified for this choice of T with the U(T²) terms included. If there exists a stabilizing continuous controller, then there also exists a stabilizing sampled-data controller for a sufficiently small choice of T     

不确定线性系统新的稳定性准则

研究了带有区间时滞的不确定系统的稳定性问题。通过采用时滞分割法,把时滞区间分割成任意两小段,并构造恰当的Lyapunov函数,利用积分不等式,得到了新的时滞相关的稳定性准则。通过数值例子验证了结果的有效性。     

Stabilizing compensator design for uncertain nonlinear systems

An observer-based control scheme is proposed for exponentially stabilizing a class of uncertain nonlinear systems. The control and observer gain expressions given in this paper resemble those used in variable-structure designs but they are continuous in nature resulting in a simple analysis of stability.     

An estimator for uncertain output matrix systems

A linear time-invariant optimal estimator for uncertain output matrix systems is considered. Uncertainty of the output matrix is represented by a set of multiple parameters, and the optimal estimator is introduced by minimizing the expected cost function of the estimation error. When the number of measured variables is small, the order of the optimal estimator does not depend on the number of models, and meeting the computational demand becomes quite feasible     

Parity relations for linear uncertain dynamic systems

A new approach for the design of parity relations for linear dynamic systems with additive and multiplicative uncertainties is presented. Instead of cancelling uncertainties following the example of the so-called robust approaches, uncertain parity relations take uncertainties into account as bounded variables. The method is based on the analysis of zonotopes representing the uncertainties. It leads both to Boolean detection results and to an indicator representing the distance to the opposite decision.     

Switching observer design for uncertain nonlinear systems

The problem of designing a switching observer for a finite or infinite set of nonlinear time-varying systems with unknown parameters and/or varying structure is studied in this paper. Under a compactness condition and a Lyapunov detectability assumption, it is shown that a switching observer with asymptotically stable error dynamics can be constructed. Different from the variable structure control method, only a finite number of switches occur before the asymptotic stability is achieved. The Lyapunov direct method is used to construct both the switching gain and the switching index. The special case where the error dynamics becomes exponentially convergent with quadratic Lyapunov detectability is also examined to illustrate the proposed observer design procedure     

Zonotopic guaranteed state estimation for uncertain systems

This paper presents a new approach for guaranteed state estimation based on zonotopes for linear discrete-time multivariable systems with interval multiplicative uncertainties, in the presence of bounded state perturbations and noises. At each sample time, the presented approach computes a zonotope which contains the real system state. A P$P$-radius-based criterion is minimized in order to decrease the size of the zonotope at each sample time and to obtain an increasingly accurate state estimation. The proposed approach allows one to efficiently handle the trade-off between the complexity of the computation and the accuracy of the estimation. An illustrative example is analyzed in order to highlight the advantages of the proposed state estimation technique.     

Sliding observer-controller design for uncertain triangularnonlinear systems

In order to achieve robust output tracking for a class of uncertain triangular systems, a combination of a robust sliding observer and a backstepping procedure is introduced     

Robust adaptive control for nonlinear uncertain systems

A direct robust adaptive control framework for nonlinear uncertain systems with constant linearly parameterized uncertainty and nonlinear state-dependent uncertainty is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic robust stability of the closed-loop system; that is, asymptotic robust stability with respect to part of the closed-loop system states associated with the plant. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.