http://control.disp.uniroma2.it/galeani/CO/materiale/automatica2000.pdf

Survey Constrained model predictive control: Stability and optimality

Time-delay systems: an overview of some recent advances and open problems

https://www.itk.ntnu.no/fag/fordypning/TK16-filer/Samling1_MorariLee.pdf

Model predictive control: past, present and future

This paper concerns a problem of robust stabilization of uncertain state-delayed systems. A new delay-dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities. An algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties.

Delay-dependent robust stabilization of uncertain state-delayed systems

Learning to act using real-time dynamic programming

Feedback controls based on the receding horizon method have proven to be a useful and easy tool in stabilizing linear ordinary differential systems. In this paper the receding horizon method is applied to linear systems with delay in the control. An open-loop optimal control which minimizes control energy subject to certain side constraints is first derived and then transformed to a closed-loop control via the receding horizon concept. The resulting feedback system is shown to be asymptotically stable under a complete controllability condition. It is also shown how the receding horizon control suggests a more general class of stabilizing feedback control laws. The control laws of this paper are perhaps the easiest way to stabilize a linear system with delay in the control.

Feedback stabilization of linear systems with delayed control

This paper considers a feedback control law for linear systems based on a minimum energy regulator problem with fixed terminal constraints on the state. A modification of this control law based on a receding horizon notion is shown to be asymptotically stable and to result in a new method for stabilizing linear time-varying systems, as well as extending some well-known methods for stabilizing time-invariant systems by state variable feedback.

A modified quadratic cost problem and feedback stabilization of a linear system

A stabilization theory which employs well-established finite-dimensional control system tools is developed for the stabilization of linear autonomous time lag systems. The main ideas include 1) a set whose elements are matrices each of which is a left zero of the system characteristic quasi-polynomial matrix, and 2) a linear transformation which reduces the delay system to a delay-free system whose state matrix is a direct sum of N elements of the matrix set where N is some positive integer. From the definition of this matrix set, it is shown that each of its elements inherits its spectrum from that of the delay system so that by design, the system unstable poles may be embedded in the spectrum of the delay-free system. Under the assumption of spectral stabilizability, it is then shown how to obtain a stabilizing feedback control law on the basis of the delay-free system. Numerical examples are presented to confirm the theory.

Feedback stabilization of linear autonomous time lag systems

Results are given for stabilizing time-varying discrete linear systems by means of a feedback control stemming from a receding-horizon concept and a minimum quadratic cost with a fixed terminal constraint. The results parallel those recently obtained for continuous-time systems [8] and extend a well-known method of Kleinman for stabilizing discrete fixed linear systems [7].

On feedback stabilization of time-varying discrete linear systems

A full state vector observer is derived for a class of linear autonomous time lag systems represented by differential equations. The major features of the approach are: (1) an observer is constructed just for the set of unstable or poorly damped modes of the delayed system once they have been determined, and (2) the design is accomplished by using a partial-fraction expansion separating the unstable part from the system and then applying well-known finite dimensional state vector techniques. A procedure for the construction is given along with some numerical results to illustrate the simplicity of the observer. >

A. E. Pearson

Papers

Feedback stabilization of linear systems with delayed control

A modified quadratic cost problem and feedback stabilization of a linear system

Feedback stabilization of linear autonomous time lag systems

On feedback stabilization of time-varying discrete linear systems

An asymptotic modal observer for linear autonomous time lag systems