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Inverse Optimal Control: A Passivity Approach
Published in Edgar N. Sanchez, Fernando Ornelas-Tellez, Discrete-Time Inverse Optimal Control for Nonlinear Systems, 2017
Edgar N. Sanchez, Fernando Ornelas-Tellez
Diverse physical systems commonly involve variables such as mass, pressure, population levels, energy, humidity, etc., which are always positive. Such systems are called positive systems, i.e., systems whose states and outputs are always nonnegative provided that the initial conditions and the input are nonnegative [15,31,45,78]. Mainly, the models representing biological processes are positive systems; perhaps the most natural examples of positive systems are the models obtained from mass balances, like the compartmental ones. This type of model is used to describe transportation, and accumulation and drainage processes of elements and compounds like hormones, glucose, insulin, metals, etc. [31].
The lq/lp Hankel norms of discrete-time positive systems across switching
Published in SICE Journal of Control, Measurement, and System Integration, 2022
This study is concerned with the analysis of the Hankel norms of discrete-time positive systems across a single switching. Early studies on positive systems focused on controllability and reachability analysis [1,2], positive realization [3,4], and positive stabilization [5]. Then, the analysis and synthesis of positive systems using convex optimization have attracted great attention, and some fruitful results have been obtained to this date. Those results include the induced norm analysis using linear programming [6,7], Kalman–Yakubovich–Popov lemma with diagonal Lyapunov variables [8,9], positive system synthesis using geometric programming [10], and positive system analysis using copositive programming [11]. Surveys on recent studies of positive systems can be found at [12,13].
Exponential stability of homogeneous impulsive positive delay systems of degree one
Published in International Journal of Control, 2021
Positive systems are systems whose states and outputs are nonnegative whenever the initial conditions and inputs are nonnegative, see Farina and Rinaldi (2000) and the references therein. Due to the fact that many practical systems involve variables (for example, absolute temperature, concentration of substances, population levels, etc.) that are intrinsically nonnegative, such systems often arise in population models, pharmacokinetics and industrial engineering, etc. Therefore in recent years, positive systems have drawn considerable research interest in the control community, see Ebihara, Peaucelle, and Arzelier (2014), Leenheer and Aeyels (2001), Nam, Phat, Pathirana, and Trinh (2016), Rami, Tadeo, and Helmke (2011), Shen and Lam (2016), Valcher (1996), Zhao, Zhang, Shi, and Liu (2012) and Zheng and Feng (2011) and the references therein.
Mean stability for a class of discrete-time non-homogeneous positive Markov jump linear systems
Published in International Journal of Systems Science, 2020
Positive systems, where the system states and outputs can take only non-negative values, have found wide applications in representing many real-world systems, e.g. economic systems, biological systems, power control systems and transportation systems (Farina & Rinaldi, 2011; Kaczorek, 2012; Zhu et al., 2019). Over the past few decades, the research of positive systems has successfully attracted lots of attention in the field of stability analysis (Liu et al., 2010; Zhao et al., 2012), filtering (Morais et al., 2018; Xiao et al., 2017), observer design (Chen et al., 2014; Rami et al., 2011; Shen & Wang, 2017), state feedback and output feedback controller design (Zhang & Jia, 2018; Zhang et al., 2014), and / performance (Briat, 2013), etc. Nowadays with the rapid increasing of the scale of aforementioned practical systems, the modelling problem is facing challenges in fully characterising the system dynamics since they are often subject to random faults or repairs of components (Li et al., 2014; Wang et al., 2014; Zhang et al., 2017). Due to the fact that the occurrence of these random events is often governed by a Markov chain, the Positive Markov Jump Linear System (PMJLS) model steps onto the stage as a result and has witnessed many meaningful achievements since its presence (Bolzern & Colaneri, 2015; Rami & Shamma, 2009; Zhu et al., 2014).