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We study the stability of a certain class of switched systems where discontinuous jumps (resets) on some of the state components are allowed, at the switching instants. It is known that, if all components of the state are available for reset, the system can be stabilizable by an adequate choice of resets. However, this question may have negative answer if there are forbidden state components for reset. We give a sufficient condition for the stabilizability of a switched system, under arbitrary switching, by partial state reset in terms of a block simultaneous triangularizability condition. Based on this sufficient condition, we show that the particular class of systems with partially commuting stable system matrices is stabilizable by partial state reset. We also provide an algorithm that allows testing whether a switched system belongs to this particular class of systems.

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Abstract. Consider a set of square real matrices of the same size A = {A 1 , A 2 , . . . , A N }, where each matrix is partitioned, in the same way, into blocks such that the diagonal ones are square matrices. Under the assumption that the diagonal blocks in the same position have a common Lyapunov solution, sufficient conditions for the existence of a common Lyapunov solution with block diagonal structure for A are presented. Furthermore, as a by-product, an algorithm for the construction of such a common Lyapunov solution is proposed.

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