Abstract
The stability problem of discrete-time switched systems with unstable modes is concerned under two novel switching strategies, i.e., limit inferior and superior Φ-dependent average dwell time switchings. Some improved stability criteria of discrete-time switched systems with unstable modes are obtained by combining a multiple Lyapunov function method with two strategies proposed, where limit inferior and superior switchings are applied to deal with stable and unstable modes, respectively. Especially, we also give stability conditions of discrete-time switched systems comprising stable modes. It is shown that these conditions with tighter bounds of average dwell time (ADT) and mode-dependent ADT cover some existing ones. Finally, two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results.
Highlights
As a special kind of hybrid systems, switched systems consist of a family of stable or unstable modes and a switching rule orchestrating the switching among modes
(3): The limit inferior DADT switching strategy we proposed is used to Discrete-time switched systems (DTSSs) with only stable modes and the corresponding stability criteria are given
Remark 9: For DTSSs composed of stable modes, it follows from Remark 4 that Theorem 4 and Corollaries 1, 2 cover the results obtained by the DADT of [26], classic modedependent ADT (MDADT) and average dwell time (ADT) approaches, respectively
Summary
As a special kind of hybrid systems, switched systems consist of a family of stable or unstable modes and a switching rule orchestrating the switching among modes. Those new concepts originate from DADT [26] and limiting ADT [27] Noting their respective shortcomings, slow and fast switching technology combined with the idea of limit inferior and superior is applied to DTSSs with stable and unstable modes. VOLUME 8, 2020 switching numbers and running time of modes 2j being activated over [v0, v], 2j ⊆ Qu. Let U = {m + 1} and U = Qu, we can obtain the following limit superior ADT and limit superior MDADT from Definition 5, respectively. We say θ (k) has a limit superior ADT (LSADT) τa∗, where Nθ (v, v0) and Kθ (v, v0) denote total switching numbers and running time of all unstable modes being activated over [v0, v]. MAIN RESULTS by exploring the property of LI DADT and LS DADT switchings, we give some more comprehensive stability results of DTSSs with unstable modes than the existing ones
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