Theoretical modeling demonstrates a linear matrix inequality control framework for implicit 2D Roesser systems, highlighting effective trajectory stabilization across continuous and discrete domains.
This article proposes a method, based on Linear Matrix Inequalities (LMI), to design a stabilising control law for a class of 2D descriptor Roesser models. Stability must be understood as the convergence of the trajectories of the model along one of the two dimensions (in practice, the time) and the models can be continuous, discrete, or mixed, i.e. one dimension is continuous while the other one is discrete. The problem is addressed by combining recent results merely concerning the stability analysis and results obtained for the control of explicit, i.e. non-descriptor, 2D Roesser models. The stabilising control law can be a basic static state feedback but can also involve the derivatives (or shifts) of the state vectors. Moreover, an integral-like term can be added to reach some steady-state requirements.
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Bachelier et al. (2026) studied this question.
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