Robust Stabilization in LMI Regions for Constrained Input Systems

Stabilization of constrained uncertain linear systems in LMI regions is studied. Robustness is in demand and exact pole assignment is no longer suitable for uncertain systems. Therefore, LMI region pole assignment encompasses the exact one preserving time domain performances in the presence of uncertainties. Robust constrained state feedback controllers are designed such that asymptotic stability and desired performances are achieved. Constraints are assumed symmetric and the LMI regions are closed under complex conjugacy. Hence, LMI's are deduced such that robust pole assignment is obtained and constraints on the input are respected. Namely, two design strategies are treated: the unsaturating and the saturating case. Optimization problem for enlarging the initial conditions set is also achieved. Simulation examples are given to show the application and the ease of the proposed approach. Comparison with different approaches for both given examples is also presented.