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In order to investigate the effects of solar radiation management (SRM) technologies for climate engineering, an analytical model describing the main latitudinal dynamics of the Earth's climate with closed-loop control has been developed. The model is a time-dependent Energy Balance Model (EBM) with latitudinal resolution and allows for the evaluation of non-uniform climate engineering strategies. The resulting partial differential equation is solved using a Green's function approach. This model offers an efficient analytical approach to design strategies that counteract climate change on a latitudinal basis to overcome regional disparities in cooling. Multi-objective analyses are considered and time-dependent analytical expressions of control functions with latitudinal resolution can be obtained in several circumstances. Results broadly comparable with the literature are found, demonstrating the utility of the model in rapidly assessing new climate engineering controls laws and strategies. For example, the model is also used to quickly assess the trade-off between the number of degrees of freedom of SRM and the rms error in latitudinal temperature compensation. Moreover, using the EBM the dynamics of the ice line can be investigated and a Lyapunov stability analysis is employed to estimate the maximum reduction of solar insolation through climate engineering before the current climate falls into an ice-covered state. This provides an extreme operational boundary to future climate engineering ventures.