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Nonlinear systems identification from experimental data without any prior knowledge of the system parameters is a challenge in control and process diagnostic. It determines mathematical model parameters that are able to reproduce the dynamic behavior of a system. This paper aims to combine two fundamental research areas: MIMO state space system identification and nonlinear control system. This combination produces a technique that leads to robust stabilization of a nonlinear Takagi–Sugeno fuzzy system (T-S).

The first part of this paper describes the identification based on the Numerical algorithm for Subspace State Space System IDentification (N4SID). The second part, from the identified models of first part, explains how we use the interpolation of linear time invariants models to build a nonlinear multiple model system, T-S model. For demonstration purposes, conditions on stability and stabilization of discrete time, T-S model were discussed.

Stability analysis based on the quadratic Lyapunov function to simplify implementation was explained in this paper. The linear matrix inequalities technique obtained from the linearization of the bilinear matrix inequalities was computed. The suggested N4SID2 algorithm had the smallest error value compared to other algorithms for all estimated system matrices.

The stabilization of the closed-loop discrete time T-S system, using the improved parallel distributed compensation control law, was discussed to reconstruct the state from nonlinear Luenberger observers.

Expansion of the consumption of renewable energy is a significant issue for reducing global warming, to cope with climate change and achieve sustainable development. This study aims to examine how research and development expenditure (R&D) affects renewable energy development in developed G-7 countries over the period from 2000 to 2019. Variables of trade liberalization and CO₂ emissions are considered control variables.

This study has adopted a panel quantile regression. The impact of the variables on renewable development has been examined in quantiles of 0.1, 0.25, 0.5, 0.75 and 0.9. Also, a robust examination is accomplished by applying generalized quantile regression (GQR).

The empirical findings reveal a positive and significant relationship between R&D and the consumption of renewable energy in 0.1, 0.25, 0.5 and 0.75 quantiles. Also, the findings describe that the expansion of trade liberalization and CO₂ emissions can significantly increase the development of renewable energy in G-7 countries. Furthermore, GQR verifies the main outcomes.

These results have very momentous policy consequences for the governments of G-7 countries. Therefore, investment and support for the R&D section to promote the development of renewable energy are recommended.

This paper, in comparison to other research, used panel quantile regression to investigate the impact of factors affecting renewable energy consumption. Also, to the best of the authors’ knowledge, no study has perused the effect of R&D along with trade liberalization and carbon emissions on renewable energy consumption in G-7 countries. Also, in this paper, as a robustness check for panel quantile regression, the GQR has been used.