Abstract
This paper studies the issue of finite-time time-varying output-feedback control for positive time-varying discrete-time linear systems. Finite-time stability for the systems with positivity is defined. To make sure that the system can be finite-time stable with positivity, an analysis condition is established first, and then two conditions for solving the static output-feedback controller are derived in this work where all the obtained results are necessary and sufficient conditions. An iterative algorithm for solving the controller is developed and finally, an example is given in the simulation to verify the effectiveness of our results and algorithm.
Highlights
In the control community, finite-time stability is a very useful and practical property of control systems, quite different from the classical Lyapunov stability that is considered in a period being infinite
A control system has the property of finite-time stability; if the initial state is given a bound, the state stays and does not leave certain bounds during a specified time interval. Such a property is commonly considered in some practical cases where, for example, large values of the state of control systems may lead to saturation (Amato et al, 2014; Mirabdollahi & Haeri, 2019)
It can be seen from many works (Amato et al, 2010a; Song et al, 2017; Xie et al, 2017; Zong et al, 2013) that the linear matrix inequality (LMI) approach is effective for solving finite-time stability problems
Summary
Finite-time stability is a very useful and practical property of control systems, quite different from the classical Lyapunov stability that is considered in a period being infinite. In the work by Amato et al (2010b), for linear time-varying continuous-time systems, finite-time stability analysis was analyzed and controller design was studied. Different from the previous work by Xue & Li (2015) and Zhu et al (2017), here, we focus on the positive time-varying discrete-time linear systems This kind of system has been studied in the recent work (Kaczorek, 2015) where the positivity and classical Lyapunov asymptotic stability were discussed. Necessary and sufficient conditions of finite-time stability and static output-feedback stabili zation for positive linear time-varying discrete-time systems are derived. BTðmÞPhðmþ1ÞBðmÞÀ qðmÞI for all h 2 f1; 2; . . . ; Jg and m 2 f0; 1; . . . ; h À 1g, ðiiiÞ PhðhÞ U, "h 2 f1; . . . ; Jg, ðivÞ Phð0Þ
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