Feedback stabilization of linear autonomous time lag systems

Fiagbedzi, Yawvi A.; Pearson, A. E.

doi:10.1109/tac.1986.1104417

Cited by 202 publications

(65 citation statements)

References 34 publications

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“…Under the infinite dimensional systems setting, references [5,6] studied continuous-time systems with a more general delay structure in both state and input than that studied in references [4,11]. Applying linear transformations, the stabilization problem for systems with single input delay was investigated in [12]. An elegant solution to the standard H ∞ control of systems with single input delay has been presented in references [13,14].…”

Section: Introductionmentioning

confidence: 99%

Infinite horizon LQR for systems with multiple delays in a single input channel

Liu

Xie

Zhang

2010

J. Control Theory Appl.

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This paper is concerned with the linear quadratic regulation (LQR) problem for both linear discrete-time systems and linear continuous-time systems with multiple delays in a single input channel. Our solution is given in terms of the solution to a two-dimensional Riccati difference equation for the discrete-time case and a Riccati partial differential equation for the continuous-time case. The conditions for convergence and stability are provided.

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Section: Introductionmentioning

confidence: 99%

Infinite horizon LQR for systems with multiple delays in a single input channel

Liu

Xie

Zhang

2010

J. Control Theory Appl.

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“…A linearized version of the feeding system and combustion chamber equations, assuming nonsteady flow, is given as follows [12]: (t) the instantaneous pressure at the place in the feeding line where the capacitance representing the elasticity is located,p 1 the value of p 1 in steady operation and p =p 1 −p the injector pressure drop in steady operation, p 0 is the regulated gas pressure for the pressure supply, P =p/(2 p), γ is the pressure exponent of the pressure dependence of the combustion process taking place during the time lag, ξ represents the fractional length for the pressure supply, J is the inertia parameter of the line, and E is the elasticity parameter of the line. Guided by [12], we take u = ( p 0 − p 1 )/(2 p) as a control variable and adopt the following representative numerical values: ξ = 0.5, γ = 1, P = 1, J = 2, E = 1, and h = 1. Letting x(t) = [ϕ(t) μ 1 (t) μ(t) ψ(t)] T , the system (21) reduces to (1) with the delay size h. It is noted that the RHC proposed in [6] cannot be applied to this system because we can not find any stability-guaranteeing terminal weighting matrices using the LMI condition proposed therein.…”

Section: A Numerical Examplementioning

confidence: 99%

An Improved Receding Horizon Control for Time-Delay Systems

Lee

Han

2014

J Optim Theory Appl

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In this paper, we propose an improved version of receding horizon control for systems with state delays. The proposed control guarantees closed-loop stability for a wider class of state-delay systems than the existing one. For expanded applications, a more generalized cost function, with three terminal weighting terms, is employed and minimized. Terminal weighting matrices are chosen to achieve the property that the optimal cost monotonically decreases with time. It turns out that the stability condition depends on the delay size and then it is less conservative than the existing delay-independent one. The simulation study shows that the proposed control scheme guarantees closed-loop stability even for state-delay systems that cannot be stabilized by the existing receding horizon control.

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“…They have investigated both continuous-time and discretetime methods for time-delay compensation proposed by other investigators [34,43] and have recommended the method proposed by Day and Hsia [34] for the design of a suitable control law. Other time-delay compensation methods that may be of interest to control of civil engineering structures are: linear predictor control [41,44,45] [58]. SOME NEW RESULTS ON COMPENSATION OF TIME DELAY To date signi"cant progress has been made in the compensation of time-delay for controlled structures.…”

Section: U(t)"gn X(t! )#Gnmentioning

confidence: 99%

Compensation of time-delay for control of civil engineering structures

Agrawal

Yang

2000

Earthquake Engng. Struct. Dyn.

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SUMMARYTime-delay is an important issue in structural control. Applications of unsynchronized control forces due to time-delay may result in a degradation of the control performance and it may even render the controlled structures to be unstable. In this paper, a state-of-the-art review for available methods of time-delay compensation is presented. Then, "ve methods for the compensation of "xed time-delay are presented and investigated for active control of civil engineering structures. These include the recursive response method, state-augmented compensation method, controllability based stabilization method, the Smith predictor method and the Pade approximation method, all are applicable to any control algorithm to be used for controlled design. Numerical simulations have been conducted for MDOF building models equipped with an active control system to demonstrate the stability and control performance of these time-delay compensation methods. Finally, the stability and performance of the phase shift method, that is well-known in civil engineering applications, have also been critically evaluated through numerical simulations.

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Feedback stabilization of linear autonomous time lag systems

Cited by 202 publications

References 34 publications

Infinite horizon LQR for systems with multiple delays in a single input channel

Infinite horizon LQR for systems with multiple delays in a single input channel

An Improved Receding Horizon Control for Time-Delay Systems

Compensation of time-delay for control of civil engineering structures

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