Guaranteed cost control for uncertain 2-D discrete systems with state delay in the Roesser model

Abstract

This paper is concerned with the problem of guaranteed cost control for uncertain two-dimensional (2-D) state delay systems described by the Roesser model. A sufficient condition for the existence of delay-dependent guaranteed cost controllers is given in terms of a linear matrix inequality (LMI) based on a summation inequality for 2-D discrete systems.A convex optimization problem is proposed to design a state feedback controller stabilizing the 2-D state delay system as well as achieving the least guaranteed cost for the resulting closed-loop system. Finally, the simulation example of thermal processes is given to illustrate the effectiveness of the proposed result.

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

“…al., 2010) is made. It is observed that the least upper bound of closed-loop cost function obtained via our approach is significantly smaller than that arrived at via previously reported approach (Xu et. al., 2010).…”

“…The problems of stability and positive observation for positive 2-D discrete-time systems in the Roesser model with multiple delays have been considered in Shen and Wang (2017). In Xu et al (2010), the guaranteed cost control problem for uncertain 2-D discrete state-delayed systems described by the Roesser model has been considered and an optimal guaranteed cost controller design method via memoryless state feedback has been established. It is worth mentioning here that if we design the optimal guaranteed cost controllers via memory state feedback with feedback provisions on current state and the past history of the state for the guaranteed cost control problem considered in Xu et.…”

“…In Section 3, an LMI-based criterion for the design of optimal guaranteed cost controllers that minimize the upper bound on the closed-loop cost function is presented. In Section 4, a comparison of the proposed criterion with previously reported criterion (Xu et. al., 2010) is made.…”

Quantification of liver fibrosis via second harmonic imaging of the Glisson's capsule from liver surface

“…The enhanced image after Frangi filtering was segmented into collagen and background by using a segmentation algorithm based on Gaussian mixture models [38], which was shown to be more accurate than other methods such as global thresholding and clustering methods [39] ( Figure 4C). The morphological closing was then performed to smooth the binary mask of the collagen and any segment with less than 5 pixels was removed ( Figure 4D).…”

Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

“…In [15], the robust stability analysis problem for a class of uncertain 2-D discrete systems described by the FM second model has been studied and sufficient conditions in terms of LMIs have been derived to ensure the robust stability of the uncertain 2-D discrete systems. Lately, the solution to the guaranteed cost control problem for 2-D discrete uncertain systems has been presented by many authors [16]- [22]. In recent years, the H ∞ control problem for 2-D discrete systems has gained a great deal of interest and many important results have been obtained [23]- [26].…”