Anti-windup design with guaranteed regions of stability for discrete-time linear systems. (English) Zbl 1129.93385
Summary: The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be locally modeled by a linear system with a deadzone nonlinearity. Then, based on the use of a new sector condition and quadratic Lyapunov functions, stability conditions in an LMI form are stated. These conditions are then considered in a convex optimization problem in order to compute an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system. Moreover, considering asymptotically stable open-loop systems, it is shown that the conditions can be slightly modified in order to determine an anti-windup gain that ensures global stability. An extension of the proposed results to the case of dynamic anti-windup synthesis is also presented in the paper.
MSC:
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 93C55 | Discrete-time control/observation systems |
| 93D15 | Stabilization of systems by feedback |
Keywords:
anti-windup; control saturation; stability; discrete-time systems; linear matrix inequalitiesReferences:
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