This article concerns the finite-time robust guaranteed cost control problem for a class of linear continuous-time singular systems with norm-bounded uncertainties. In this study, the problem is to design a state feedback controller such that the closed-loop system is finite-time stable, and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. By constructing an appropriate Lyapunov function, a sufficient condition for the finite-time robust stability of the system based on linear matrix inequality (LMI) is established. Furthermore, the sufficient condition for the existence of the guaranteed cost controller is formulated in terms of LMIs, which can make the closed-loop uncertain singular system finite-time robust stable. Finally, two numerical examples are given for illustration of the proposed theoretical results.
BackgroundIdentification of risk factors that have causal effects on the occurrence of diabetic kidney disease (DKD), is of great significance in early screening and intervening for DKD, and in delaying the progression of DKD to end-stage renal disease. Cathepsin S (Cat-S), a novel non-invasive diagnostic marker, mediates vascular endothelial dysfunction. The diagnostic value of Cat-S for DKD has rarely been reported in clinical studies.ObjectiveTo analyze whether Cat-S is a risk factor for DKD and evaluate the diagnostic value of serum Cat-S for DKD.MethodsForty-three healthy subjects and 200 type 2 diabetes mellitus (T2DM) patients were enrolled. T2DM patients were divided into subgroups according to various criteria. Enzyme-linked immunosorbent assay was used to detect serum Cat-S levels among different subgroups. Spearman correlation analysis was used to analyze correlations between serum Cat-S and clinical indicators. Multivariate logistic regression analysis was performed to analyze risk factors for the occurrence of DKD and decreased renal function in T2DM patients.ResultsSpearman analysis showed that serum Cat-S level was positively correlated with urine albumin creatinine ratio (r=0.76, P<0.05) and negatively correlated with estimated glomerular filtration rate (r=−0.54, P<0.01). Logistic regression analysis showed that increased serum Cat-S and cystatin C(CysC) were independent risk factors for DKD and decreased renal function in T2DM patients (P<0.05). The area under the receiver operating characteristic (ROC) curve was 0.900 of serum Cat-S for diagnosing DKD, and when the best cut-off value was 827.42 pg/mL the sensitivity and specificity were 71.6% and 98.8%, respectively. Thus, serum Cat-S was better than CysC for diagnosing DKD (for CysC, the area under the ROC curve was 0.791, and when the cut-off value was 1.16 mg/L the sensitivity and specificity of CysC were 47.4% and 98.8%, respectively).ConclusionIncreased serum Cat-S were associated with the progression of albuminuria and decreased renal function in T2DM patients. The diagnostic value of serum Cat-S was better than that of CysC for DKD. Monitoring of serum Cat-S levels could be helpful for early screening DKD and assessing the severity of DKD and could provide a new strategy for diagnosing DKD.
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