Sufficient LMI conditions for H<inf>&#x221E;</inf> static output feedback control of 2-D systems

Abstract

This paper investigates the problems of H∞ static output feedback (SOF) control of two-dimensional (2-D) discrete systems described by the Roesser model and FornasiniMarchesini second model, respectively. By applying the 2-D Bounded Real Lemma combined with a slack variable technique, some sufficient linear matrix inequality (LMI)-based conditions for the existence of SOF controllers are established. Numerical examples are given to illustrate the effectiveness of the proposed LMI-based design method.Index Terms-2-D discrete systems, H ∞ control, static output feedback, linear matrix inequality (LMI).

H∞ Static Output Feedback Control of 2‐D Discrete Systems in FM Second Model

“…It is worth mentioning that the solution of LMI is affected by the choosing of coordinate transformation matrix Γ b 1 . This point is important in solving LMI , however, it is not addressed in . Remark Note that the structure of the slack variable is different from the structures of the slack variables used in and . In , the slack variables are taken as scalar matrices, i.e ., scalar multiples of the identity matrices.…”

“…It is seen from Table that the LMI method of failed to find a solution for this example. Using Theorem with Γ 12 being chosen as a null matrix, the numerical result obtained is example the same as that obtained by using Theorem .…”

“…Inspired by the idea of , Feng et al . proposed some sufficient LMI conditions for the H ∞ SOF control problems of both the 2‐D Roesser model and the 2‐D FM second model. In , the slack variables introduced are taken as scalar matrices, which leads to conservativeness.…”

A Survey on H∞ Control-Based Output Feedback Techniques

“…Controlling through the output feedback technique is most appropriate in such situations. This has led many studies [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] to investigate and analyze output feedback techniques for 2-D discrete systems.…”

Delay-Dependent Robust &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;∞&lt;/sub&gt; Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

“…In [24], the solutions for the H ∞ control and robust stabilization problems for 2-D systems described by the Roesser model using the 2-D system bounded realness property have been presented. The problem of H ∞ static output feedback control for 2-D discrete systems described by the Roesser model and the FM second model has been addressed in [25]. In [26], the problem of robust H ∞ control for uncertain 2-D discrete systems described by the GM via output feedback controllers has been investigated.…”