Static Output Feedback Stabilization of Multiple Models Subject to Actuators Saturation D. SAIFIA*, M. CHADLI** S. LABIOD * ** LAMEL, Faculté des Sciences et de la Technologie, Université de Jijel BP. 98, Ouled Aissa 18000 Jijel - Algeria( Email: {Saifia79 , labiod_salim}@yahoo.fr) ** Université de Picardie Jules Verne, MIS (EA 4290)7, Rue du Moulin Neuf - 80000: Amiens – France Phone: (33) 3 22 82 76 80 - Fax: (33) 3 22 82 76 68, Email: mohammed.chadli@u-picadrie.fr Abstract: This paper deals with the stabilization of multiple models under actuator saturation analysis via a static output feedback control law. The multiple model approach is used to represent the nonlinear system by interpolation of local linear models. The control inputs are subject to actuators saturation in polytopic modeling. The set of invariance condition for static output feedback system under actuator saturation is first established. The estimation of the largest domain of the attraction for this system is formulated and solved as a linear matrix inequality (LMI) optimization problem. A numerical example is given to show the effectiveness of the proposed method. Keywords: Actuators saturation, multiple models, stabilization, static output feedback, linear matrix inequality. 1. INTRODUCTION The multiple models is an effective approach to approximating nonlinear systems by interpolation of numerous local linear models (Murray-Smith and Johansen 1997, Chadli 2002). Generally, the multiple models has been controlled by the so-called parallel distributed compensation (PDC) (Murray-Smith and Johansen 1997, Chadli and Maquin 2002, Cao and Lin 2003, Han 2007 and Kim et al. 2009). However, state variables are not always fully measurable for most industrial plants in practice (Zhang et al. 2009). Output feedback can provide an effective approach for designing nonlinear control systems (Chadli and Maquin 2002, Chadli and Borne 2007 and Zhang et al. 2009). On other hand, all actuators have physical limitations. These limitations result in constraints and saturation on their amplitudes and/or their velocities. Actuator saturation can degrade the performance of closed-loop system and often make the stable closed loop system unstable. Thus, the implementation of control laws designed without taking into account the saturation effect may have undesirable consequences on the system behavior. This problem has been receiving increasing attention for control of both linear (Jomas da Silva 1997, Henrion and Tarbouriech 1999, Kapoor and Daoutidis 2000, Jomas da Silva, and Tarbouriech 2006, Eugênio et al 2008 and Hu et al 2008) and nonlinear (Cao and Lin 2003, Han 2007, Kim et al 2009, Zhang et al. 2009, Ohtake et al. 2009, Du and Zhang 2009) systems. The saturation limits are avoided by designing low gain control laws that, for a given bound on the initial conditions (Cao and Lin 2003, Han 2007). The using of this method will often result low levels of performance (Cao and Lin 2003). The problem is dealt by estimating the domain of attraction of closed-loop system with the presence of saturation (Cao and Lin 2003 et al. 2009, Zhang et al. 2009). Very often, the saturation effect is represented by polytopic model ( Cao and Lin 2003, Han 2007, Kim et al. 2009) or is transformed into deadzone nonlinearity (Zhang et al. 2009). Based on this representation and using the set invariance condition, the analysis and synthesis of control system with actuator saturation is formulated and solved as a linear matrix inequality (LMI) optimization problem (Cao and Lin 2003, Han 2007, Kim et al. 2009, Zhang et al. 2009). In our knowledge, the static output feedback of multiple models under actuator saturation is not fully studied, which is the aim of our contribution. This paper deals with the static output feedback stabilization of nonlinear systems in multiple models representation under actuator saturation. The saturation effect is represented by a polytopic model. The problem of estimating the largest domain of attraction for static output feedback system with actuator saturation is formulated and solved as a linear matrix inequality (LMI) optimization problem. This paper is organized as follows. Section 2 gives the mathematical description of multiple models with static output feedback in the presence of saturation. Section 3 formulates the conditions for stabilization in term of LMIs. Finally, in section 4 the numerical example is used to show the effectiveness of the proposed method.