Design of Sliding Mode Control with observer based Linear Matrix Inequlity for input saturation system

This thesis is a research report on the design of observer on anti windup system with multivariable Sliding Mode Control (SMC) controller. The design is done in three stages, the first stage is the multivariable SMC controller design that gives the L and S constants, the second stage is the static anti windup compensator design to overcome the directionality problem, and the third stage is the full order observer design than gives observer gain (K). These three stages are done with Linear Matrix Inequality (LMI). The saturation effect that leads to the inconsistency between control input and controller´s state when the control signal is saturated is called windup. This phenomenon can leads to the degradation on the system´s performance. There is also another phenomenon that need to be considered, which is when not all the states can be achieved from sensors. But, if the system is controllable and observable, this problem can be solved by using an observer. Observer with Lyapunov Stability Criterion has been successfully designed. The simulation of the observer design showed good result which shows the transient of the state error to zero at a certain time. Lyapunov stability and L₂ - gain performance criteria also succeeded in reducing the effect of saturation in the system.