Robust Filtering and Control of 2-D State-Delayed Systems: A Delay-Dependent Approach

This dissertation studies the robust filtering and control problems for two-dimensional (2-D) state-delayed systems in the Fornasini-Marchesini second model by using a delay-dependent approach. A 2-D system is one that has dynamics depending on two independent integer variables i and j. 2-D signals and systems
have become more and more important in the fields like image processing, digital signal
processing, and process control. The study of 2-D systems has attracted increasing attentions in recent years. A particular case
of 2-D systems, 2-D state-delayed systems, can be found in many
practical applications such as the material rolling process, partial
difference equation modeling, and image data processing/transmission. Thus the
analysis and synthesis of 2-D state-delayed systems are
worthwhile investigation issues. The main focus of this research is the use of
linear matrix inequality (LMI) techniques for both analysis and
synthesis problems.

Firstly, a computationally tractable
sufficient condition for the asymptotic stability of 2-D state-delayed systems, which depend on the
size of delays in both horizontal and vertical directions, are
derived in terms of LMIs. Then, delay-dependent H-infinity performance and H-2 performance criteria are proposed. Based on the results,
efficient methods to solve the robust H-infinity filtering,
H-2 filtering, and mixed H-2/H-infinity
filtering problems are developed. Differently from the quadratic stability
framework, the filter design methods in this dissertation adopt the parameter-dependent
Lyapunov function approach, which utilizes different Lyapunov matrices
in the entire polytope domain and produces less
conservative design results.

Finally, the state feedback controller synthesis problem for the system is also considered.
A new delay-dependent robust stability condition is derived,
and used to develop a robust stabilization method. The goal is to find a state feedback controller
such that the closed-loop system is robustly stable for all
admissible uncertainties.