Reduced-order observers for linear neutral delay systems

The problem of reduced-order observers design for linear neutral delay systems is investigated. Sufficient conditions for the existence of these observers are given. First, the general case is presented, then under more restrictive conditions a simple design method is developed for some special cases. Based on linear matrix inequality (LMI) and linear matrix equality (LME) formulation, independent of delays stability criteria are derived. A systematic design method of these observers is presented.     

含参数不确定性的马尔可夫跳变过程鲁棒正实控制

讨论一类具有随机跳变参数的线性系统正实控制问题,其跳变参数的跃迁由有限状 态的马尔可夫过程描述.基于随机李亚普诺夫函数的方法,并结合线性矩阵不等式,分别提出依 赖于模态的状态反馈和输出反馈控制,以保证相应闭环系统的严格正实性.进一步针对系统含 参数不确定性的情形,引入鲁棒正实性分析,得到鲁棒正实控制器存在的充分条件和设计方法.     

Disturbance Decoupled Observers for Systems With Unknown Inputs

This note deals with the design of reduced-order disturbance decoupled scalar functional observers for linear systems with unknown inputs. Based on a parametric approach, existence conditions are derived and a design procedure for finding reduced-order scalar functional observers is given. The derived existence conditions are relaxed and the procedure can find first-order disturbance decoupled scalar functional observers for some cases where the number of unknown inputs is more than the number of outputs. Also, the observer matching condition, which is the necessary requirement for the design of state observers for linear systems with unknown inputs, is not required. Numerical examples are given to illustrate the attractiveness of the proposed design method.      

Robust observer design for nonlinear uncertain systems with LQ regulators

For a class of uncertain systems with linear nominal dynamics and nonlinear uncertainties, it has been shown (Katayama and Sasaki 1987) that linear quadratic (LQ) state feedback regulators can be used to provide robust asymptotic stability. In this paper, we study the combined observer-controller design problem, based on the linear state feedback regulator proposed by Katayama and Sasaki (1987), so that only output feedback is needed. Both full-order and reduced-order observers are considered. For the full-order observer, we propose an algorithm to synthesize the robust observer gain matrix. It is shown that with the observer it is still possible to achieve robust asymptotic stability. For the reduced-order observer, some conditions are derived to guarantee the robust asymptotic stabilizability of the uncertain systems. The trade-off between the magnitudes of controller and observer gains is clear in our approach. An example is used to illustrate the design process of the robust controller with full-order as well as reduced-order observers.     

Delayed Observers for Linear Systems With Unknown Inputs

We present a method for constructing reduced-order state observers for linear systems with unknown inputs. Our approach provides a characterization of observers with delay, which eases the established necessary conditions for existence of unknown input observers with zero-delay. We develop a parameterization of the observer gain that decouples the unknown inputs from the estimation error, and we use the remaining freedom to ensure stability of the error dynamics. Our procedure is quite general in that it encompasses the design of full-order observers via appropriate choices of design matrices     

Partial-State Observers for Nonlinear Systems

This note deals with the design of reduced-order observers for a class of nonlinear systems. The order reduction of the observer is achieved by only estimating a required partial set of the state vector. Necessary and sufficient conditions are derived for the existence of reduced-order observers. An observer design procedure based on linear matrix inequalities is given. A numerical example is given to illustrate the design method     

Partial state and unknown input estimation for time-delay systems

This article considers the problem of estimating a partial set of the state vector and/or unknown input vector of linear systems driven by unknown inputs and time-varying delay in the state variables. Three types of reduced-order observers, namely, observers with delays, observers without internal delays and delay-free observers are proposed in this article. Existence conditions and design procedures are presented for the determination of parameters for each case of observers. Numerical examples are presented to illustrate the design procedures.     

Robust reduced-order sliding mode observer design

In this article, a triple state and output variable transformation-based method combined with linear matrix inequality (LMI) techniques to design a new robust reduced-order sliding mode observer for perturbed linear multiple-input and multiple-output systems is developed. The state and output variables of the original system are triple transformed into suitable canonical form coordinates to facilitate the design of a reduced-order observer. The existing transformations are summarised in this study and presented systematically. A new combined observer configuration is proposed and compared with another type of observers. Global asymptotical stability LMI and sliding mode existence conditions for the coupled observer error system are derived using Lyapunov full quadratic form. Reaching and sliding modes of motion of decoupled observer error system are discussed as well. Two numerical and simulation examples are given to illustrate the usefulness of the proposed design techniques.     

Quasi-ISS/ISDS observers for interconnected systems and applications

This paper considers interconnected nonlinear dynamical systems and studies observers for such systems. For single systems the notion of quasi-input-to-state dynamical stability (quasi-ISDS) for reduced-order observers is introduced and observers are investigated using error Lyapunov functions. It combines the main advantage of ISDS over input-to-state stability (ISS), namely the memory fading effect, with reduced-order observers to obtain quantitative information about the state estimate error. Considering interconnections quasi-ISS/ISDS reduced-order observers for each subsystem are derived, where suitable error Lyapunov functions for the subsystems are used. Furthermore, a quasi-ISS/ISDS reduced-order observer for the whole system is designed under a small-gain condition, where the observers for the subsystems are used. As an application, we prove that quantized output feedback stabilization for each subsystem and the overall system is achievable, when the systems possess a quasi-ISS/ISDS reduced-order observer and a state feedback law that yields ISS/ISDS for each subsystem and therefor the overall system with respect to measurement errors. Using dynamic quantizers it is shown that under the mentioned conditions asymptotic stability can be achieved for each subsystem and for the whole system.     

Linear functional observers for systems with delays in State variables: the discrete-time case

This note extends to the discrete-time case the design of linear functional state observers, recently developed for continuous-time delay systems. Sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear and bilinear matrix inequalities [(LMIs) and (BMIs)] formulations.     

Design of reduced-order observers without internal delays

This paper provides a simple and systematic design method of reduced-order observers without internal delays for systems having a time delay in the state variables. Necessary and sufficient conditions for the existence of these observers are given     

UNKNOWN INPUTS OBSERVERS DESIGN FOR DELAY SYSTEMS

This paper concerns the design of functional, reduced and full order observers for linear time delay systems with unknown inputs. A new method generalizing those existing in the literature is presented for systems with unknown inputs, these unknown inputs are present in both the state and the measurement equations. Conditions for the existence of these observers are given and sufficient conditions for the stability independent of delays are derived using linear matrix‐inequality (LMI) formulation. The independent of internal delay and independent of delay cases are also presented. A numerical example is presented to illustrate our approach.     

Delay-dependent stabilization of singularly perturbed jump linear systems

This paper considers the stability and stabilization problems of continuous-time singularly perturbed Markov jump linear systems. LMI-based sufficient conditions for the system to be stochastically stable are given, and using LMI approaches, two methods for designing state feedback stabilizing controllers are also derived. Numerical examples are worked out to illustrate the usefulness of the proposed results.     

Robust stability,stabilization and ℋ∞ control of time‐delay systems with Markovian jump parameters

In this paper, the problems of stochastic stability and stabilization for a class of uncertain time‐delay systems with Markovian jump parameters are investigated. The jumping parameters are modelled as a continuous‐time, discrete‐state Markov process. The parametric uncertainties are assumed to be real, time‐varying and norm‐bounded that appear in the state, input and delayed‐state matrices. The time‐delay factor is constant and unknown with a known bound. Complete results for both delay‐independent and delay‐dependent stochastic stability criteria for the nominal and uncertain time‐delay jumping systems are developed. The control objective is to design a state feedback controller such that stochastic stability and a prescribed ?_∞‐performance are guaranteed. We establish that the control problem for the time‐delay Markovian jump systems with and without uncertain parameters can be essentially solved in terms of the solutions of a finite set of coupled algebraic Riccati inequalities or linear matrix inequalities. Extension of the developed results to the case of uncertain jumping rates is also provided. Copyright © 2003 John Wiley & Sons, Ltd.     

Stability analysis and stabilization of networked linear systems with random packet losses

This paper is concerned with the stability analysis and stabilization of networked discrete-time and sampled-data linear systems with random packet losses. Asymptotic stability, mean-square stability, and stochastic stability are considered. For networked discrete-time linear systems, the packet loss period is assumed to be a finite-state Markov chain. We establish that the mean-square stability of a related discrete-time system which evolves in random time implies the mean-square stability of the system in deterministic time by using the equivalence of stability properties of Markovian jump linear systems in random time. We also establish the equivalence of asymptotic stability for the systems in deterministic discrete time and in random time. For networked sampled-data systems, a binary Markov chain is used to characterize the packet loss phenomenon of the network. In this case, the packet loss period between two transmission instants is driven by an identically independently distributed sequence assuming any positive values. Two approaches, namely the Markov jump linear system approach and randomly sampled system approach, are introduced. Based on the stability results derived, we present methods for stabilization of networked sampled-data systems in terms of matrix inequalities. Numerical examples are given to illustrate the design methods of stabilizing controllers.     

Optimal linear estimation for continuous stochastic systems with random observation delays

This paper is concerned with the linear minimum mean square error estimation for Itô‐type differential equation systems with random delays, where the delay process is modeled as a finite‐state Markov chain. By first introducing a set of equivalent delay‐free observations and then defining two reorganized Markov chains, the estimation problem of random delayed systems is reduced to the one of delay‐free Markov jump linear systems. The estimator is derived by using the innovation analysis method based on the Itô differential formula. And the analytical solution to this estimator is given in terms of two Riccati differential equations that are of finite dimensions. Conditions for existence, uniqueness, and stability of the steady‐state optimal estimator are studied for time‐invariant cases. In this case, the obtained estimator is very easy to implement, and all calculation can be performed off line, leading to a linear time‐invariant estimator. Copyright © 2011 John Wiley & Sons, Ltd.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.     

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality(LMI). Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.