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This paper deals with H∞ filtering for two-dimensional (2-D) discrete-time linear parameter-varying systems described by the Fornasini-Marchesini second model with matrices that depend rationally on convex-bounded time-varying parameters. A method is proposed for the design of robust 2-D filters with a prescribed H∞ performance for all admissible parameters' trajectories. The filter design method...
Fundamental structural properties are identified for a class of implicit two-dimensional (2-D) system models with a form that is closed under static local-state feedback and output-injection transformations. The structural properties are investigated in terms of quater-plane causal solutions given compatible boundary conditions, controlled and conditioned invariants, and the corresponding output-nulling...
In this paper, we show how the purity filtration of a finitely presented module, associated with a multidimensional linear system, can be explicitly characterized by means of classical concepts of module theory and homological algebra. Our approach avoids the use of sophisticated homological algebra methods such as spectral sequences used in [3], [4], [5], associated cohomology used in [9], and Spencer...
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