Separation principle for quasi‐one‐sided Lipschitz nonlinear systems with time delay

In this article, we address the problem of output stabilization for a class of nonlinear time‐delay systems. First, an observer is designed for estimating the state of nonlinear time‐delay systems by means of quasi‐one‐sided Lipschitz condition, which is less conservative than the one‐sided Lipschitz condition. Then, a state feedback controller is designed to stabilize the nonlinear systems in terms of weak quasi‐one‐sided Lipschitz condition. Furthermore, it is shown that the separation principle holds for stabilization of the systems based on the observer‐based controller. Under the quasi‐one‐sided Lipschitz condition, state observer and feedback controller can be designed separately even though the parameter (A,C) of nonlinear time‐delay systems is not detectable and parameter (A,B) is not stabilizable. Finally, a numerical example is provided to verify the efficiency of the main results.     

Robust H∞ sliding mode observer‐based fault‐tolerant control for One‐sided Lipschitz nonlinear systems

This paper presents fault tolerant controllers for a class of one‐sided Lipschitz nonlinear systems with external disturbances. A sliding mode observer (SMO) is integrated with the H_∞ filtering approach as the fault detection and isolation module. The problem is investigated in the presence of faults and disturbances simultaneously. The H_∞ ‐SMO is capable of approximating faults accurately, while reducing the effect of disturbances in the estimation of the state vector and occurred faults. Accordingly, using only a single SMO, the estimation error of the state vector and faults can be made simultaneously arbitrarily small. In addition, to deal with the weighted bilinear form appearing in the one‐sided Lipschitz condition, the quadratically inner bounded condition presented in the literature is employed in this paper as a useful solution. The proposed method guarantees the stability of the overall closed‐loop system, and after a short transient time, the estimation errors for state vector and fault signal converge to a small neighborhood of the origin. The effectiveness of the presented algorithm is confirmed in two examples including a single arm robot with a flexible joint and a numerical simulation.     

Observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinearities

This paper discusses the observer‐based finite‐time stabilization for discrete‐time switched singular systems with quadratically inner‐bounded nonlinear terms. Firstly, based on the Luenberger‐like observer, by using the average dwell time approach, sufficient conditions are proposed to make closed‐loop systems be regular, be causal, as having a unique solution, and be uniformly finite‐time bounded. Then, a new linear matrix inequality sufficient condition for the existence of an observer‐based controller is obtained by using certain matrix decoupling techniques, and the controller is designed. In this paper, the conditions proposed not only give the observer‐based controller design methods but also guarantee the existence and uniqueness of solution for the systems. Since the quadratically inner‐bounded nonlinearities are more general than Lipschitz nonlinearities and one‐sided Lipschitz nonlinearities, compared with previous works, the proposed controller design methods in this paper are also more general than the existing ones. Finally, numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

Finite‐Time H∞ Filtering for Nonlinear Continuous‐Time Singular Semi‐Markov Jump Systems

The stochastic finite‐time H_∞ filtering issue for a class of nonlinear continuous‐time singular semi‐Markov jump systems is discussed in this paper. Firstly, sufficient conditions on singular stochastic H_∞ finite‐time boundedness for the filtering error system are established. The existence of a unique solution for the corresponding system is also ensured. Secondly, based on the bounds of the time‐varying transition rate, without imposing constraints on slack variables, a novel approach to finite‐time H_∞ filter design is proposed in the forms of strict LMIs, which guarantees the filtering error system is singular stochastic H_∞ finite‐time bounded and of a unique solution. Compared with the existing ones, the presented results reveal less conservativeness. Finally, one numerical example is exploited to testify the advantage of the proposed design technique.     

LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME‐DELAY SYSTEMS WITH NONLINEAR DISTURBANCES

This paper investigates the problem of robust filtering for a class of uncertain nonlinear discrete‐time systems with multiple state delays. It is assumed that the parameter uncertainties appearing in all the system matrices reside in a polytope, and that the nonlinearities entering into both the state and measurement equations satisfy global Lipschitz conditions. Attention is focused on the design of robust full‐order and reduced‐order filters guaranteeing a prescribed noise attenuation level in an H∞ or l₂‐l∞ sense with respect to all energy‐bounded noise disturbances for all admissible uncertainties and time delays. Both delay‐dependent and independent approaches are developed by using linear matrix inequality (LMI) techniques, which are applicable to systems either with or without a priori information on the size of delays.     

Nonlinear observer design for one‐sided Lipschitz systems with time‐varying delay and uncertainties

This paper investigates the problem of state observer design for a class of nonlinear uncertain dynamical systems with interval time‐varying delay and the one‐sided Lipschitz condition. By constructing the novel Lyapunov–Krasovskii functional while utilizing the free‐weighting matrices approach, the one‐sided Lipschitz condition and the quadratic inner‐bounded condition, novel sufficient conditions, which guarantee the observer error converge asymptotically to zero, are established for a class of nonlinear dynamical systems with interval time‐varying delay in terms of the linear matrix inequalities. The computing method for observer gain matrix is given. Finally, two examples illustrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

Composite disturbance‐observer‐based control and H ∞ control for nonlinear time‐delay systems

A novel type of control scheme combined the distance‐observer‐based control (DOBC) with H_∞ control is proposed for a class of nonlinear time‐delay systems subject to disturbances. The disturbances are supposed to include two parts. One in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other is supposed to have the bounded H₂ norm. The disturbance observers based on regional pole placement and D‐stability theory are presented, which can be designed separately from the controller design. By integrating disturbance‐observer‐based control with H_∞ control laws, the disturbances can be rejected and attenuated, simultaneously, the desired dynamic performances can be guaranteed for nonlinear time‐delay systems with unknown nonlinear dynamics. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H∞ Filtering For Uncertain Stochastic Time‐Delay Systems

This paper deals with the problem of robust H_∞ filtering for uncertain stochastic systems. The system under consideration is subject to time‐varying norm‐bounded parameter uncertainties and unknown time delays in both the state and measurement equations. The problem we address is the design of a stable filter that ensures the robust stochastic stability and a prescribed H_∞ performance level for the filtering error system irrespective of all admissible uncertainties and time delays. A suffient condition for the solvability of this problem is proposed and a linear matrix inequality approach is developed for the design of the robust H_∞ filters. An illustrative example is provided to demonstrate the effctiveness of the proposed approach.     

Fault detection for a class of discrete‐time nonlinear systems subject to network‐induced uncertainties

This paper addresses the problem of fault detection (FD) for discrete‐time systems with global Lipschitz conditions and network‐induced uncertainties. By utilizing Bernoulli stochastic variables and a switching signal, a unified measurement model is proposed to describe three kinds of network‐induced uncertainties, that is, access constraints, time delays, and packet dropouts. We aim to design a mode‐dependent fault detection filter (FDF) such that, for all external disturbances and the above uncertainties, the error between the residual and fault is made as small as possible. The addressed FD problem is then converted into an auxiliary H_∞ filtering problem for discrete‐time stochastic system with multiple time‐varying delays. By applying the Lyapunov‐Krasovskii approach, a sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMI). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the results obtained. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society