New system identification methods are developing constantly to come up with solutions that can take into account all of the factors that real-time systems have. These factors affect the analysis of the system’s behavior, particularly noise, non-linearities, system’s complexity, time varying changes, among others. This thesis is concerned with system identification methods related to a nuclear norm pareto optimization. These algorithms try to join 2 families of system identification methods, the PEM and SID, this with the purpose of trying to find a balance or trade-off between the complexity of the system identified and the goodness of the fitting criterion. The nuclear norm heuristics are used widely as a convex approximation for the RMP. In this work it will be used for system identification purposes; were a new low rank matrix and fitting criterion formulation is constructed inspired by the PBSIDopt algorithm. This algorithm will rename and stack data to construct a matrix that thanks to the properties assumed in the system it can be defined as a upper triangular lowrank matrix. The objective is to see if this method brings any benefits compared to the already existent low rank matrix mechanisms that are inspired by structural analysis or the instrumental variables and/or projections methods. A step further was taken to provide the framework for this method named N2PBSID algorithm by providing the steps necessary for the implementation of this optimization problem on MATLAB. Lastly, several experiments are performed and a number of conclusions are drawn from them. Making an assessment on the effectiveness of the algorithm, the feasibility of its performance based on the difficulties encountered and final thoughts and recommendations.