Abstract
This paper addresses the problems of robust stability analysis and L1-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L1-gain performance of the considered system without control inputs, and several stability conditions and L1-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L1-gain performance is satisfied simultaneously. Furthermore, to make the controller synthesis problem numerically tractable, we propose an iterative convex optimization algorithm to compute the desired controller parameters. Finally, three numerical examples and two realistic examples are presented to show the effectiveness and applicability of the proposed methodology.
Highlights
With approximately 8.8 million cancer-related deaths and 14 million new cancer cases per year, at present neoplastic diseases are a significant cause of morbidity and mortality worldwide
Improvement of nutrition has been shown to positively affect heart rate variability (HRV), too (Hansen et al, 2014). This manuscript is the first to systematically compile and appraise on how HRV is associated with cancer progression and the value of HRV in predicting cancer patients’ prognosis
The majority of the studies indicate that a decreased HRV is common in cancer patients, likely reflecting autonomic dysfunction associated with the disease
Summary
With approximately 8.8 million cancer-related deaths and 14 million new cancer cases per year, at present neoplastic diseases are a significant cause of morbidity and mortality worldwide. Data on prognostic factors are integral to improve patients’ specific prognosis (Gidron et al, 2014). Prognostic factors such as tumor stage and tumor markers [e.g., prostate-specific antigen (PSA), alpha-fetoprotein (AFP), human chorionic gonadotropin (hCG)] have been shown to correlate with the course of disease and/or prognosis (Mead and Stenning, 1997; Gospodarowicz and O’Sullivan, 2003). There are many other host-related or environmental factors (e.g., pollution, nutrition) which may affect the
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