LMIs in Control/Click here to continue/Optimal control systems/Discrete time H2 optimal filter

Introduction The goal of optimal filtering is to design a filter that acts on the output z of the generalized plant and optimizes the transfer matrix from w to the filtered output. An H2-optimal filter is designed to minimize the norm of (will be defined below). System Dynamics Consider the discrete-time generalized LTI plant with minimal states space realization where it is assumed that A_{d} is Schur. A discrete-time dynamics LTI filter with state-space realization is to be designed to optimize the transfer function from w{k} to , given by , where The Optimization Problem Solve for that minimize subject to LMI < 0 , < 0 , Conclusion The filter is recovered by the state-space matrices