1c:I[419806,["/_next/static/chunks/bb923814e1f4d2e9.js","/_next/static/chunks/dd3ee9f5b7716ca6.js","/_next/static/chunks/4204a0ae82542ca8.js","/_next/static/chunks/30036bedc5269936.js","/_next/static/chunks/6e1aa89a642f40be.js","/_next/static/chunks/cd5e572bc3e4eb92.js","/_next/static/chunks/8ffd0b71567920d8.js","/_next/static/chunks/67ea6dfd21f16c5f.js","/_next/static/chunks/24eb4379f68013fd.js","/_next/static/chunks/b8cd775ffdf935bd.js","/_next/static/chunks/983103cd9eb7b428.js","/_next/static/chunks/d4ac9dcf27f6ff52.js","/_next/static/chunks/294b9525248c8e5f.js"],"default"] 1d:T46c,During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.1e:T4fe, This paper first investigates the stability and $l_{2}$-gain problems for a class of discrete-time switched systems with average dwell time (ADT) switching by allowing the Lyapunov-like functions to increase during the running time of subsystems. The obtained results then facilitate the studies on the issue of asynchronous control, where “asynchronous” means the switching of the controllers has a lag to the switching of system modes. In light of the proposed Lyapunov-like functions, the desired mode-dependent controllers can be designed since the unmatched controllers are allowed to perform in the interval of asynchronous switching before the matched ones are applied. The problem of asynchronous $H_{\infty}$ control for the underlying systems in linear cases is then formulated. The conditions of the existence of admissible asynchronous $H_{\infty}$ controllers are derived, and a numerical example is provided to show the potential of the developed results. 1f:T5d7,

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