Abstract
This paper is concerned with control synthesis of uncertain Roesser-type discrete-time two-dimensional (2D) systems. The mathematical model of the 2D system’s parameter uncertainty, which may appear typically in many actual environment, is modeled as a convex bounded uncertain domain. By using the Lyapunov stability theory, stabilization conditions is proposed in with the purpose of ensuring the robust asymptotical stability of the underlying closed-loop uncertain Roesser-type discrete-time 2D systems. Furthermore, the obtained result of this paper is formulated in the form of linear matrix inequalities (LMIs), which can be easily solved via standard numerical software. Finally, a numerical example is also provided to demonstrate the effectiveness of the proposed result.
Highlights
Over the past several decades, the 2D systems have attracted considerable research interests due to their wide applications in many areas such as water stream heating, thermal processes, biomedical imaging, data processing and transmission, multidimensional digital filters, image processing, grid based wireless sensor networks [1, 2]
The so-called 2D modeling theory could be applied as an efficient analysis tool to deal with other problems; for example, elimination of overflow oscillations in 2D digital filters employing saturation arithmetic has been implemented be means of linear matrix inequalities (LMIs) in [6], LMI-based stability analysis of 2D discrete systems described by the Fornasini-Marchesini (FM) second model with state saturation has been addressed in [7], H∞ filter design for 2D Markovian jump systems has been given in [8], and optimal guaranteed cost control of 2D discrete uncertain systems has been studied in [9], respectively
Considering the fact that state saturation often appears in various 2D digital systems when its transfer function is implemented by a state-space model with the finite wordlength format, the problem of stability analysis of 2D state-space digital filters with saturation arithmetic has been deeply investigated in the literature [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] and less conservative LMI-based stability criteria have been persistently obtained
Summary
Over the past several decades, the 2D systems have attracted considerable research interests due to their wide applications in many areas such as water stream heating, thermal processes, biomedical imaging, data processing and transmission, multidimensional digital filters, image processing, grid based wireless sensor networks [1, 2]. The earlier results on stability analysis and control synthesis of linear uncertain systems were obtained by applying the common quadratic Lyapunov function (CQLF). Due to the complexity of mathematical analysis, there has been few work on control synthesis of linear uncertain Roessertype discrete-time 2D systems in the existing literature so far. This problem needs to be further investigated and this fact motivates us to carry out the investigation proposed in this paper. Motivated by the above analysis, the problem of control synthesis of uncertain Roesser-type discrete-time twodimensional systems will be investigated based on the Lyapunov stability theory in this paper. X > 0 (or X ≥ 0) denotes the matrix X as symmetric and positive definite (or symmetric and positive semidefinite); a star ∗ in a symmetric matrix represents the transposed element in the symmetric position; XT means the transpose of X; the symbol I denotes the identity matrix with appropriate dimension
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