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

Abstract

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.

A differential‐free output feedback control for stabilization of continuous‐time LTI systems with Euler's approximation method

“…In the continuous-time LTI system (1), if and only if there exists a constant vector F such that the time-delayed control system (9) is asymptotically stable then the control law (5) would asymptotically stabilize the closed-loop system.…”

“…Then, the differential-free output feedback controller (5) can stabilize the continuous-time LTI system (1). Furthermore, the time-delayed system (9) would be asymptotically stable.…”

“…Hence, it cannot be directly applied in some practical systems. Thus, the observer (state estimator) has been suggested to estimate the states in the practical control systems . Then, a state‐feedback control policy combining with a state observer may be preferred in control applications.…”

“…Thus, the observer (state estimator) has been suggested to estimate the states in the practical control systems. 1,2 Then, a state-feedback control policy combining with a state observer may be preferred in control applications. In the linear dynamical systems, it is shown that the controller and observer design would be independent of each other.…”

Interval observers for linear functions of state vectors of linear fractional‐order systems with delayed input and delayed output

“…In this case, the estimation of actual states and output feedback control law are very necessary. This problem for systems with integer order has been extensively investigated (see, for example, other works [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] ). For fractional-order systems, some interesting results on the observer design for fractional-order systems were reported in related works.…”