S-procedure for deriving stability conditions of hybrid Roesser models

Abstract

In this paper, the so-called full block Sprocedure is applied to propose a general methodology that enables the derivation of LMI stability conditions for a quite general class of multidimensional linear systems, namely those described by hybrid Roesser models.

Finite‐region stability and finite‐region boundedness for 2D Roesser models

“…which implies Remark We note that the inequalities and are not LMIs. We will apply procedures proposed in to convert conditions and into solvable LMIs conditions. We set R = I and impose the following constrains: for l = 1,2, and to simplify conditions and as follows: Obviously, LMIs conditions – guarantee and , so the FRS of the system with respect to ( c , c 1 , c 2 , I 1 × I 2 , R ) can be checked via the following theorem.Theorem Given positive scalars c , c 1 , c 2 with c 1 + c 2 < c , I 1 , I 2 ∈ N + and a positive definite matrix R , the 2D system is FRS with respect to ( c , c 1 , c 2 , I 1 × I 2 , R ), if for l = 1,2, there exist scalars α l >0, β l >0, a l >0, b l >0, μ l >0, matrices P l >0, Q l >0, and 0 < η < 1 satisfying c 1 < η c , such that conditions – and – are fulfilled.…”

“…We note that the inequalities (6) and (7) are not LMIs. We will apply procedures proposed in [6] to convert conditions (6) and (7) into solvable LMIs conditions. We set R D I and impose the following constrains: for l D 1, 2,…”

“…In recent decades, discrete two‐dimensional (2D) models have been widely applied in iterative learning, image processing, satellite cloud picture analysis, seismological and geographical data processing, X‐ray image enhancement, and other fields . Lyapunov asymptotic stability (LAS) theory is commonly considered to be a fundamental and an important aspect of 2D models; after decades of development, research on the topic has become quite sophisticated and received several notable achievements. For example, stability analysis problems for 2D systems have been successfully investigated in as well as stabilization and H ∞ control problems for 2D systems with Markovian jump parameters .…”

Input–output finite-region stability and stabilization for discrete 2-D Fornasini–Marchesini models

“…In recent decades, discrete two-dimensional (2-D) models have been widely applied in iterative learning, image processing, satellite cloud picture analysis, seismological and geographical data processing, X-ray image enhancement, and other fields [1][2][3]. As is well known, Lyapunov asymptotic stability (LAS) theory [4][5][6][7] is a fundamental and important control issue for 2-D models. After decades of development, research on this topic has become quite sophisticated and has witnessed several notable achievements.…”