Control of uncertain system represented by polytope using enhaced Lyapunov function

Lately, it has been developed many studies related to the control of uncertain systems, one reason for this studies is because it is hard to precisely describe a system, therefore the process is expressed as uncertain systems. One way to represent an uncertain system is by describing the model as a convex combination of several knownmodels. In this paper a state feedback controller is designed for an uncertain plant using a parameter dependent Lyapunov function V(X) = X
^T
P(α)X that guaranties less conservative LMIs. A way to restrict the closed loop poles based on a decay rate is also applied for the enhanced Lyapunov function. Finally this paper minimizes the norm of a controller using the parameter dependent Lyapunov function for uncertain system. Practical results are obtained by implementing the enhanced Lyapunv function in the inverted pendulum of Quanser
^®
company.