A fresh approach to the design of observers for time-delay systems

2016 ◽  
Vol 40 (2) ◽  
pp. 477-503 ◽  
Author(s):  
Dinh Cong Huong
Keyword(s):  
Time Delay ◽  
State Vector ◽  
State Observer ◽  
The State ◽  
Observer Design ◽  
Delay Systems ◽  
Time Delay Systems ◽  
State Variables ◽  
State Transformation ◽  
Original State

This paper presents a fresh approach to the design of state observers for a class of time-delay systems with one time delay in the state and output vectors. By proposing a new coordinate state transformation, the system is first transformed into the new coordinates where all the delay terms associated with the state variables are injected into the system’s output and input. Thus, in the new coordinate system, a Luenberger-type state observer can be easily designed. Then, a backward state transformation problem is studied which allows us to reconstruct the original state vector of the system. Conditions for the existence of the state transformations and an algorithm for computing them are provided in this paper. We show that our approach works for a wider class of time-delay systems in the sense that when some existing state observer design methods fail to reconstruct the state vector, the proposed new change of coordinates and the observer scheme in this paper can still reconstruct the original state vector. Numerical examples and simulation results are given to illustrative the effectiveness of the proposed design approach.

scholarly journals New delay-dependent observer-based control for uncertain stochastic time-delay systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiu-feng Miao ◽  
Long-suo Li
Keyword(s):  
Time Delay ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Noise Disturbances ◽  
System States ◽  
Delay Dependent ◽  
Stochastic Time

AbstractThis paper considers the problem of estimating the state vector of uncertain stochastic time-delay systems, while the system states are unmeasured. The system under study involves parameter uncertainties, noise disturbances and time delay, and they are dependent on the state. Based on the Lyapunov–Krasovskii functional approach, we present a delay-dependent condition for the existence of a state observer in terms of a linear matrix inequality. A numerical example is exploited to show the validity of the results obtained.

scholarly journals New observer-based control design for mismatched uncertain systems with time-delay

2016 ◽  
Vol 26 (4) ◽  
pp. 597-610 ◽  
Author(s):  
Van Van Huynh
Keyword(s):  
Time Delay ◽  
Estimation Error ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
State Matrix ◽  
Control Techniques ◽  
Uncertain Time

Abstract In this paper, the state estimation problem for a class of mismatched uncertain time-delay systems is addressed. The estimation uses observer-based control techniques. The mismatched uncertain time-delay systems investigated in this study include mismatched parameter uncertainties in the state matrix and in the delayed state matrix. First, based on a new lemma with appropriately choosing Lyapunov functional, new results for stabilization of mismatched uncertain time-delay systems are provided on the basis of a linear matrix inequality (LMI) framework and the asymptotic convergence properties for the estimation error is ensured. Second, the control and observer gains are given from single LMI feasible solution which can overcome the drawback of the bilinear matrix inequalities approach often reported in the literature. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.

Discretized Lyapunov-Krasovskii Functional for Systems With Multiple Delay Channels

2008 ◽  
Author(s):  
Hongfei Li ◽  
Keqin Gu
Keyword(s):  
Time Delay ◽  
Standard Form ◽  
Computational Effort ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
State Variables ◽  
Regular Time ◽  
Low Dimensional ◽  
Necessary And Sufficient

Many practical systems have a large number of state variables but only a few components have time delays. These delay components are often scalar or low dimensional, and involve single time delay in each component. A coupled differential-difference equation is well suited to formulate such systems. It is known that such a formulation is very general. Systems with multiple related or independent delays can be transformed into this standard form. Similar to regular time-delay systems, the existence of a quadratic Lyapunov-Krasovkii functional is necessary and sufficient for stability. This article discusses the discretization of such a quadratic Lyapunov-Krasovskii functional. Even for time-delay systems of retarded type, the formulation has significant advantage over the traditional formulation, as the size of the resulting linear matrix inequalities are drastically reduced for such systems. Indeed, the computational effort needed for checking stability of such a large system with a few low dimensional delays is quite reasonable.

scholarly journals Design of the State Predictive Model Following Control System with Time-Delay

2009 ◽  
Vol 19 (2) ◽  
pp. 247-254 ◽  
Author(s):  
Dazhong Wang ◽  
Shujing Wu ◽  
Shigenori Okubo
Keyword(s):  
Control System ◽  
Time Delay ◽  
Predictive Model ◽  
The State ◽  
Delay Systems ◽  
Control Synthesis ◽  
Time Delay Systems ◽  
Model Following Control ◽  
Model Following ◽  
System With Time Delay

Design of the State Predictive Model Following Control System with Time-DelayTime-delay systems exist in many engineering fields such as transportation systems, communication systems, process engineering and, more recently, networked control systems. It usually results in unsatisfactory performance and is frequently a source of instability, so the control of time-delay systems is practically important. In this paper, a design of the state predictive model following control system (PMFCS) with time-delay is discussed. The bounded property of the internal states for the control is given, and the utility of this control design is guaranteed. Finally, examples are given to illustrate the effectiveness of the proposed method, and state predictive control techniques are applied to congestion control synthesis problems for a TCP/AQM network.

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