This paper addresses the problem of designing a control law to stabilize planar (i.e. second order) linear switched autonomous systems when a delay affects the switching instants. The stability of the delayed system is investigated under the assumption that the corresponding deterministic system is stabilized by a switching table. This table is obtained by minimizing a performance metric that is a functional of the norm of the state. It is formally proved that for not necessarily bounded random delays, a linear switched autonomous non-Markovian system is still stable for a sufficiently small value of the multiplier parameter connected to the random delay. We also determine numerically the multiplier parameter value which discriminates stable and unstable behaviors for uniform and normal delay distribution and suggest a method for construction of the switching table based on minimizing the convergence rate.

本文讨论了设计控制律以在延迟影响切换时刻时稳定平面（即二阶）线性切换自治系统的问题。在相应的确定性系统由交换表稳定的假设下，研究了时滞系统的稳定性。通过最小化作为国家规范的功能的性能指标来获得该表。正式证明，对于不一定受限的随机延迟，对于与随机延迟相连的乘数参数足够小的值，线性切换自主非马尔可夫系统仍然稳定。