Design Techniques of Linear Constrained Discrete-Time Control Systems

An Optimization Approach to the Design of Constrained Regulators for Uncertain Discrete-Time Systems

“…It is also assumed that the vector q = [q 1 q 2 · · · q p ] T belongs to a bounded symmetric and convex polyhedral set Q ⊂ R p . This set can also be defined either by a set of linear inequalities of the form Hq ≤ f or as the convex hull of its vertices q (1) , q (2) , . .…”

“…In this case the derivation of stabilizing control laws is a rather difficult problem. [1][2][3] Two different classes of constrained control problems have been the object of most of the papers. The first class of problems is related to the determination of a control law and of set of admissible states so that all the initial states belonging to this set are transferred to the origin asymptotically while state and control constraints are respected.…”

“…1,3,9,10,12 Most of the approaches to this problem are based on the properties of positively invariant polyhedral sets. 11,12 In fact, the control law is determined so that the a priori given set of initial states is a positively invariant set of the resulting controlled system.…”

A polyhedral approach to the stability analysis and feedback stabilization of networked control systems

“…This Lemma is an extension to uncertain systems of a basic result developed for time-invariant systems [17]. Relations (12) and (13) …”

Feedback stabilization of Networked Control Systems

“…In the best of the authors' knowledge, the use of polyhedral Lyapunov functions has not yet been investigated in the context of NCS, although it has been shown to be a powerful tool in many interesting control problems (including the case of robust and constrained control) where it yields generic and less conservative results compared to quadratic Lyapunov approaches [12], [13], [14], [15]. In this paper NCSs are described by ARMA models.…”