Lqg Control of Lpv Systems with Parameter-dependent Lyapunov Function

A LQG control design technique for LPV systems using single Lyapunov function is improved by searching for a parameter-dependent Lyapunov function in order to enhance the LQG performance of the control. Such a design technique has not been developed in the LQG framework so far (in the authors knowledge), albeit its adaptability to performance degradation on the parameter region enlarges the class of systems that the method can be applied for. The solution of the LQG LPV problem is based on parameter-dependent stability that is guaranteed by searching for a parameter-dependent Lyapunov function for the closed loop. The LQG cost function is minimized simultaneously. The problem is equivalent to the minimization of a linear function subject to LMI constraints. The improvement of the performance is presented on a simple example.