Estimation of the potential GDP by a new robust filter method.

The first purpose of this paper is to propose a theoretically new robust filter method to estimate non-observable macroeconomic indicators. The second purpose is to apply the proposed method to estimate the Hungarian potential GDP in 2000-2021. The novelty of the proposed filter method is that - unlike papers published so far - it does not require the stability of the dynamic model, only a partial stability condition must be satisfied. Moreover, such time-dependent uncertainties and nonlinearities can arise in the model that satisfy a general quadratic constraint. An important advantage of the proposed robust filter method over the traditional Kalman filter is that no stochastic assumptions is needed that may not be valid for the problem at hand. The proposed filter method has never been applied to estimate the potential GDP. To estimate the Hungarian potential GDP, the proposed method is applied using uni-, bi- and trivariate models. Estimations up to 2021 has not been published yet for the Hungarian economy. The examined period includes both the financial world crisis and the Covid-19 crisis. The results of the different models are consistent. It turned out that the economic policy was very procyclical after 2012, and the GDP gap was still positive during and also after the Covid-19 crisis.

Dynamic output feedback H∞ design in finite-frequency domain for constrained linear systems.

This paper deals with the design problem of H∞ control for linear systems in finite-frequency (FF) domain. Accordingly, the H∞ norm from the exogenous disturbance to the controlled output is reduced in a given frequency range with utilizing the generalized Kalman-Yakubovic-Popov (gKYP) lemma. As some of the states are hard or impossible to measure in many applications, a dynamic output feedback controller is proposed. In order to meet practical requirements that express the limitations of the physical system and the actuator, these time-domain hard constraints are taken into account in the controller design. An algorithm terminating in finitely many steps is given to determine the dynamic output feedback with suboptimal FF H∞ norm bound. The algorithm consists of solving a series of linear matrix inequalities (LMIs). Finally, two case studies are given to demonstrate the effectiveness and advantageous of the proposed method.