A course of H∞0Econtrol theory
A course of H∞0Econtrol theory
The H∞ control problem
Automatica (Journal of IFAC)
Linear quadratic suboptimal control with static output feedback
Systems & Control Letters
Output feedback stabilizability and stabilization algorithms for 2D systems
Multidimensional Systems and Signal Processing
Robust and optimal control
Feedback Stabilizability of MIMO n-D Linear Systems
Multidimensional Systems and Signal Processing
Solutions for H_{\infty} Filtering of Two-DimensionalSystems
Multidimensional Systems and Signal Processing
One- and Multidimensional Signal Processing: Algorithms and Applications in Image Processing
One- and Multidimensional Signal Processing: Algorithms and Applications in Image Processing
Two-Dimensional Digital Filters
Two-Dimensional Digital Filters
Multidimensional Systems and Signal Processing
A direct-construction approach to multidimensional realization and LFR uncertainty modeling
Multidimensional Systems and Signal Processing
H∞ filtering of 2-D discrete systems
IEEE Transactions on Signal Processing
Brief H∞ control and robust stabilization of two-dimensional systems in Roesser models
Automatica (Journal of IFAC)
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This paper presents a comprehensive investigation on the $${{\mathcal H}_{\infty}}$$ control problem of linear multidimensional (nD) discrete systems described by the nD Roesser (local) state-space model. A Bounded Real Lemma consisting of a series of conditions is first established for general nD systems. The proposed nD conditions directly reduce to their 1D counterparts when n = 1, and besides several sufficient conditions which include the existing 2D results as special cases, some necessary and sufficient conditions are also shown to explore further insights to the considered problem. By applying a linear matrix inequality (LMI) condition of the nD Bounded Real Lemma, the nD $${{\mathcal H}_{\infty}}$$ control problem is then considered for three kinds of control laws, namely, static state feedback (SSF) control, dynamic output feedback (DOF) control and static output feedback (SOF) control, respectively. The nD $${{\mathcal H}_{\infty}}$$ SSF and DOF control problems are formulated in terms of an LMI and LMIs, respectively, and thus tractable by using any available LMI solvers. In contrast, the solution condition of the nD $${{\mathcal H}_{\infty}}$$ SOF controller is not strictly in terms of LMIs, therefore an iterative algorithm is proposed to solve this nonconvex problem. Finally, numerical examples are presented to demonstrate the application of these different kinds of nD $${{\mathcal H}_{\infty}}$$ control solutions to practical nD processes as well as the effectiveness of the proposed methods.