Nonlinear H∞ observer design for one‐sided Lipschitz discrete‐time singular systems with time‐varying delay

This paper investigates the H_∞ observer design problem for a class of nonlinear discrete‐time singular systems with time‐varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one‐sided Lipschitz condition and quadratically inner‐bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality–based approach for the nonlinear observer design is proposed. The resulting nonlinear H_∞ observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance γ. The synthesis condition of H_∞ observer design for nonlinear discrete‐time singular systems without time delays is also presented. The design is first addressed for one‐sided Lipschitz discrete‐time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.     

Observer design for nonlinear discrete‐time systems: Immersion and dynamic observer error linearization techniques

This paper focuses on the observer design for nonlinear discrete‐time systems by means of nonlinear observer canonical form. At first, sufficient and necessary conditions are obtained for a class of autonomous nonlinear discrete‐time systems to be immersible into higher dimensional observer canonical form. Then a method called dynamic observer error linearization is developed. By introducing a dynamic auxiliary system, the augmented system is shown to be locally equivalent to the generalized observer form, whose nonlinear terms contain auxiliary states and output of the system. A constructive algorithm is also provided to obtain the state coordinate transformation. These results are an extension of their counterparts of nonlinear continuous‐time systems to nonlinear discrete‐time systems (Syst. Control Lett. 1986; 7 :133–142; SIAM. J. Control Optim. 2003; 41 :1756–1778; Int. J. Control 2004; 77 :723–734; Automatica 2006; 42 :321–328; IEEE Trans. Automat. Control 2007; 52 :83–88; IEEE Trans. Automat. Control 2004; 49 :1746–1750; Automatica 2006; 42 :2195–2200; IEEE Trans. Automat. Control 1996; 41 :598–603; Syst. Control Lett. 1997; 31 :115–128). Copyright © 2009 John Wiley & Sons, Ltd.     

Using set invariance to design robust interval observers for discrete‐time linear systems

Based on interval and invariant set computation, an interval version of the Luenberger state observer for uncertain discrete‐time linear systems is proposed in this work. This new interval observer provides a punctual estimation of the state vector and guaranteed bounds on the estimation error. An off‐line and an on‐line approach to characterize, in a guaranteed way, the estimation error are introduced. Compared with the existing approaches, the proposed interval observer design method is not restrictive in terms of required assumptions, complexity, and on‐line computation time. Furthermore, the convergence issue of the estimation error is well established and to reduce the conservatism of the estimated state enclosure induced by the bounded additive state disturbance and noise measurement, an H_∞ method to compute the optimal observer gain is proposed. The performance of the proposed state estimation approach are highlighted on different illustrative examples.     

Decoupling Controller with Disturbance Observer for LTI MIMO Systems

In this paper, a decoupling multivariable control strategy for linear time‐invariant (LTI) multi‐input/multi‐output (MIMO) systems is proposed. The strategy includes a multivariable disturbance observer (MDOB) and a decoupling controller. This MDOB is introduced to improve the system performances when the system encounters severe external disturbances. H₂ optimal scheme is utilized to design the MDOB filter. The controller is developed based on an inverse control method, through which the design process can be simplified. Simulation results certify the effectiveness of the proposed control strategy.     

L∞ Observer for Uncertain Linear Systems

In this paper, an L_∞ observer design method is proposed for linear system subject to parameter uncertainty and bounded disturbance. The proposed L_∞ observer, which satisfies a peak‐to‐peak disturbances attenuation performance, is designed to overbound the estimation error. Moreover, sufficient conditions for the design of L_∞ observer are derived and expressed in terms of linear matrix inequalities (LMIs). The novelty of the proposed method is that we develop an L_∞ observer that not only can attenuate bounded disturbance but also provides an upper bound of estimation error norm. Simulation results are presented to illustrate the effectiveness of the proposed method.     

Secure estimation for cyber‐physical systems with adversarial attacks and unknown inputs: An L2‐gain method

This paper investigates the attack‐resilient state estimation problem for linear systems with adversarial attacks and unknown inputs, where the upper bound of the unknown inputs is unknown. It is assumed that the attacker has limited resources and can only manipulate a certain number of sensors. In most of the existing observer design approaches for the systems with unknown inputs even in the absence of attacks, the observer matching condition should be satisfied. To overcome this restriction, a novel switched observer is proposed, where the matched unknown inputs will be completely compensated by means of the outputs and the mismatched part will be suppressed in terms of L₂‐gain rejection property. Meanwhile, the observer can provide an attack‐resilient state estimation. Compared with the existing results, the proposed observer can guarantee that the resulting observer error system is stable with unknown input attenuation level γ that can be optimized. Finally, a simulation example of an unmanned ground vehicle is provided to show the effectiveness of the proposed approach.     

Robust Unknown Input Observer Design for Linear Uncertain Time Delay Systems with Application to Fault Detection

In this paper, a novel approach is proposed to design a robust fault detection observer for uncertain linear time delay systems. The system is composed of both norm‐bounded uncertainties and exogenous signals (noise, disturbance, and fault) which are considered to be unknown. The main contribution of this paper is to present unknown input observer (UIO)‐based fault detection system which shows the maximum sensitivity to fault signals and the minimum sensitivity to other signals. Since the system contains uncertainty terms, an H_∞ model‐matching approach is used in design procedure. The reference residual signal generator system is designed so that the fault signal has maximum sensitivity while the exogenous signals have minimum sensitivity on the residual signal. Then, the fault detection system is designed by minimizing the estimation error between the reference residual signal and the UIO residual signal in the sense of H_∞ norm. A sufficient condition for the existence of such a filter is exploited in terms of certain linear matrix inequalities (LMIs). Application of the proposed method in a numerical example and an engineering process are simulated to demonstrate the effectiveness of the proposed algorithm. Simulation results show the validity of the proposed approach to detect the occurrence of faults in the presence of modeling errors, disturbances, and noise.     

Dynamic output feedback sliding mode control for nonminimum phase linear systems with disturbance attenuation

A sliding mode control algorithm using output information only is developed in this paper for a linear system with mismatched disturbance. The nominal system is allowed to be nonminimum phase. A scheme designed to combine the output‐dependent integral sliding surface with a reduced‐order observer is proposed. Utilizing an H_∞ control analytical technique, once the system is in the sliding mode, the proposed algorithm can guarantee robust stabilization and sustain the nature of performing disturbance attenuation when the solution to one algebraic Riccati inequality can be found. A controller is designed to satisfy the reaching and sliding condition in line with the reduced‐order observer. Finally, a numerical example is explained to show the applicability of the proposed scheme. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Delay‐range‐dependent robust H∞ filtering for uncertain systems with interval time‐varying delays

This paper is concerned with the problem of delay‐range‐dependent robust H_∞ filtering for systems with time‐varying delays in a range. The aim of this problem is to design a filter such that, for all admissible uncertainties, the filtering error system is robustly asymptotically stable with a prescribed H_∞ level. The desired filter can be constructed by solving a set of linear matrix inequalities (LMIs). An illustrative numerical example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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     

Exponential H∞ filter design for stochastic time‐varying delay systems with Markovian jumping parameters

In this paper, the exponential H_∞ filter design problem is investigated for a general class of stochastic time‐varying delay system with Markovian jumping parameters. The stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time‐varying. Attention is focused on the design of mean‐square exponentially stable and Markovian jump filter such that the filtering error systems are mean‐square exponentially stable and the estimation error satisfies a given H_∞ performance. By introducing some slack matrix variables, delay‐dependent sufficient conditions for the solvability of the above problem are presented in terms of linear matrix inequalities (LMIs). In addition, the decay rate can be a given positive value without any other constraints. When the proposed LMIs are feasible, an explicit expression of the desired H_∞ filter can be given. A numerical example is provided to illustrate the effectiveness of the proposed design approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust MIMO disturbance observer analysis and design with application to active car steering

A multi‐input–multi‐output extension of the well‐known two control degrees‐of‐freedom disturbance observer architecture that decouples the problem into single‐input–single‐output disturbance observer loops is presented in this paper. Robust design based on mapping D‐stability and the frequency domain specifications of weighted sensitivity minimization and phase margin bound to a chosen controller parameter space is presented as a part of the proposed design approach. The effect of the choice of disturbance observer Q filter on performance is explained with a numerical example. This is followed by the use of structured singular values in the robustness analysis of disturbance observer controlled systems subject to structured, real parametric and mixed uncertainty in the plant. A design and simulation study based on a four wheel active car steering control example is used to illustrate the methods presented in the paper. Copyright © 2009 John Wiley & Sons, Ltd.     

Sampled‐data H∞ control for networked systems with random packet dropouts

This paper is concerned with the H_∞ control problem for networked control systems (NCSs) with random packet dropouts. The NCS is modeled as a sampled‐data system which involves a continuous plant, a digital controller, an event‐driven holder and network channels. In this model, two types of packet dropouts in the sensor‐to‐controller (S/C) side and controller‐to‐actuator (C/A) side are both considered, and are described by two mutually independent stochastic variables satisfying the Bernoulli binary distribution. By applying an input/output delay approach, the sampled‐data NCS is transformed into a continuous time‐delay system with stochastic parameters. An observer‐based control scheme is designed such that the closed‐loop NCS is stochastically exponentially mean‐square stable and the prescribed H_∞ disturbance attenuation level is also achieved. The controller design problem is transformed into a feasibility problem for a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust fuzzy control for continuous perturbed time‐delay affine takagi–sugeno fuzzy models

The stability analysis and controller synthesis methodology for a continuous perturbed time‐delay affine (CPTDA) Takagi–Sugeno (T‐S) fuzzy model is proposed in this paper. The CPTDA T‐S fuzzy models include both linear nominal parts and uncertain parameters in each fuzzy rule. The proposed fuzzy control approach is developed based on an iterative linear matrix inequality (ILMI) algorithm to cope with the stability criteria and H_∞ performance constraints for the CPTDA T‐S fuzzy models. Finally, a numerical simulation for the nonlinear inverted pendulum system is given to show the application and availability of the present design approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust H∞ fuzzy observer‐based tracking control design for a class of nonlinear stochastic Markovian jump systems

This paper investigates the stochastic H_∞ tracking control problem for a class of nonlinear stochastic Markovian jump systems. The attention is focused on the design of a fuzzy observer‐based fuzzy controller such that an H_∞ model reference tracking performance is guaranteed for admissible disturbances. A sufficient condition is established to guarantee the existence of the desired robust controller, which is given in terms of a set of coupled matrix inequalities. Moreover, a novel decoupled method is proposed to transform the sufficient condition into some linear matrix inequality (LMI) form such that observer gains and control gains can be simultaneously obtained by solving a set of LMIs. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust L2−L∞ Filtering for Stochastic Systems with Discrete and Distributed Time‐Varying Delays

This paper is devoted to the problem of robust L₂–L_∞ filtering for a class of stochastic systems with both discrete and distributed time‐varying delays. The objective is to design a full‐order filter such that the resulting filtering error system is stochastically asymptotically stable with a prescribed L₂–L_∞ performance satisfied. Delay‐dependent sufficient condition for the existence of the filter is obtained in terms of linear matrix inequalities (LMIs). And the filter design method is proposed, while the explicit expression for the desired filter is also given. Numerical examples are included to illustrate the benefit and the effectiveness of the proposed method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

An interval observer for uncertain continuous‐time linear systems

To design robust interval observers for uncertain continuous‐time linear systems, a new set‐integration approach is proposed to compute trajectory tubes for the estimation error. Because this approach, the order‐preserving condition on the dynamics of the estimation error is no longer required. Therefore, synthesis methods can be used to compute observer gains that reduce the impact of the system uncertainties on the accuracy of the estimated state enclosures. The performance of the proposed approach is showcased through illustrative numerical examples.