Abstract
The linear quadratic Gaussian (LQG) control for one-dimensional (1D) systems has been known to be one of the fundamental and significant methods in linear system theory. However, the LQG control problem for two-dimensional (2D) systems has not been satisfactorily solved due to their structural and dynamical complexity. In this paper, sufficient conditions for evaluation of the quadratic performance indices of 2D systems in terms of the system state and control variables are proposed. Using these conditions, systematic design methods for finite horizon and infinite horizon LQG controls of 2D systems are developed using a convex optimization method.
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Yang, R., Zhang, C. & Xie, L. Linear quadratic Gaussian control of 2-dimensional systems. Multidim Syst Sign Process 18, 273–295 (2007). https://doi.org/10.1007/s11045-006-0016-6
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DOI: https://doi.org/10.1007/s11045-006-0016-6