Uniform ultimate boundedness analysis and synthesis for linear systems with dead-zone in the actuators
Résumé
The presence of the dead-zone nonlinearity is common in many physical systems and in general degrades the control systems performance or stability. This note considers an interconnection between a continuous time multiple-input linear system and a dead-zone nonlinearity associated with a state feedback. The issue of analyzing the property of uniform ultimate boundedness (UUB) of a system and the issue of designing a control under UUB constraint are studied. Firstly, the dead-zone is replaced via a linear transformation introducing the saturation. Secondly, we improve the size of the UUB area that can be found in the literature, by expressing the saturation in terms of parametrized piecewise affine bounds. This allows also a link between standard approaches such ones using piecewise affine models or ones considering global cone bounded sector conditions. In the framework of analysis and synthesis, sufficient conditions are obtained by linear matrix inequalities. Illustrative examples are given to spotlight the efficiency of our approach.