In this paper, the index-1 notion for arbitrarily switched discrete-time linear singular systems (SDLS) has been introduced. Based on the Bohl exponents of SDLS as well as properties of associated positive switched systems, some necessary and sufficient conditions have been established for exponential stability. | VNU Journal of Science: Mathematics – Physics, Vol. 34, No. 4 (2018) 84-91 Stability of Arbitrarily Switched Discrete-time Linear Singular Systems of Index-1 Pham Thi Linh* VNU University of Science, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam Received 22 December 2018 Revised 27 December 2018; Accepted 28 December 2018 Abstract: In this paper, the index-1 notion for arbitrarily switched discrete-time linear singular systems (SDLS) has been introduced. Based on the Bohl exponents of SDLS as well as properties of associated positive switched systems, some necessary and sufficient conditions have been established for exponential stability. Keywords: Switched system, linear discrete-time singular system, positive system, index-1 system. 1. Introduction Recently there has been a great interest in arbitrarily switched discrete-time linear singular systems due to their importance in both theoretical and practical aspects, see [5, 10, 13, 15], and the references therein. Consider a switched system consisting of a set of subsystems and a rule that describes switching among them. It is well known that, even if all linear descriptor subsystems are stable but inappropriate switching may make the whole system unstable. On the other hand, since abrupt changes in system dynamics may be caused by unpredictable environmental factors or component failures, it is important to require the stability for some real-life switched systems under arbitrary switching. It should be noted that although there are a few works devoted to stability analysis of SDLS, see [5, 13, 15], to our best of knowledge, the problem of investigating the stability for such switched systems via their Bohl exponents or properties of associated positive switched systems has not yet been studied before. Thus, this work was intended as an attempt to fill this gap. 2. Switched discrete-time linear singular systems of index-1 Consider the following autonomous SDLS of the form: _ Tel.: 84-336112702. Email:
