Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

Abstract

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

Robust output tracking of nonlinear systems with transient improvement via funnel-based sliding mode control

“…The most important control objectives that have been considered in the control of dynamic systems are improving the robustness of systems, improving transient responses, and reducing the steady-state error. To achieve the desired characteristic of the control system, there are several control methods such as sliding mode control (Binazadeh and Shafiei, 2013, 2014; Dastaviz and Binazadeh, 2019, 2020; Mohammadpour and Binazadeh, 2018; Shtessel et al, 2014), Lyapunov redesign (Binazadeh and Rahgoshay, 2016; Kamarudin et al, 2019), H ∞ control (Gholami and Binazadeh, 2019; Aidoud and Sedraoui 2018; Saravanakumar et al, 2018), adaptive control (Adloo and Shafiei 2019; Azhdari and Binazadeh, 2020; Guo and Wen, 2011) and Linear matrix inequality (LMI)-based control (Asadinia and Binazadeh, 2019; Baleghi and Shafiei, 2018; Motahhari and Shafiei, 2020) that focus on the robustness of the closed-loop systems in the presence of uncertain terms and/or external disturbances. These methods have usually been designed based on Lyapunov analysis to meet the desired system performances that lead to the elimination of steady-state error in tracking or regulation problems.…”

Event-triggered control of positive Markov jump systems without/with input saturation

“…Positive systems, whose state variables and outputs always keep non-negative if the initial states and inputs take non-negative values (Farina and Rinaldi, 2000; Lam et al, 2019; Luenberger, 1979), have attracted much attention in economics, communications, chemical engineering process, network employing and TCP, and so on. Some interesting topics on positive systems have been explored in Ait Rami (2011), Cavalanti and Balakrishnan (2020), Chen et al (2018), Fornasini and Valcher (2012), Gurvits et al (2007), Knorn et al (2009), Liu et al (2019), Ocampo-Martinez et al (2013), Motahhari and Hossein Shafiei (2020) and Zhu et al (2019). Positive Markov jump systems are a special class of Markov jump systems (Bouskas, 2005; Costa et al, 2005; Zong and Ren, 2019a), which consist of positive subsystems and a Markov process.…”