Asynchronous switching differing from asynchronous consensus may hinder the system to reach a consensus. This receives very limited attention, especially when the multi-agent systems have a controller fault. In order to analyze the consensus in this situation, this paper studies the consensus of the second-order multi-agent systems under asynchronous switching with a controller fault. We convert the consensus problems under asynchronous switching into stability problems and obtain important results for consensus with the aid of linear matrix inequalities. An example is given to illustrate the effect of asynchronous switching on the consensus, and to validate the analytical results in this paper.

Integrated sensing and communications (ISAC) is emerging as a critical technique for next-generation communication systems. Reconfigurable intelligent surface (RIS) can simultaneously enhance the performance of communication and sensing by introducing new degrees-of-freedom for beamforming in ISAC systems. This paper proposes two optimization techniques for joint beamforming in RIS-assisted ISAC systems. We first aim to maximize the radar mutual information (MI) by imposing constraints on communication rate, transmit power, and unit modulus reflection coefficients at the RIS. An alternating optimization (AO) algorithm based on the semidefinite relaxation (SDR) method is proposed to solve the optimization problem by introducing a convergence-accelerating method. To achieve lower computational complexity and better reliability, we then formulate a new optimization problem for maximizing the weighted ISAC performance metrics under fewer constraints. An AO algorithm based on the Riemannian gradient (RG) method is proposed to solve this problem. This is achieved by reformulating the transmit and RIS beamforming on the complex hypersphere manifold and complex circle manifold, respectively.Numerical results show that the proposed algorithms can enhance the radar MI and the weighted communication rate simultaneously. The AO algorithm based on RG exhibits better performance than the SDR-based method. I. INTRODUCTION Many emerging applications for future networks, such as vehicle-to-everything and smart homes, require high-quality communication performance and demand accurate sensing capabilities [1], [2]. The communication and sensing functionality can be simultaneously realized in a unified platform due to their similar hardware architecture and signal processing algorithms. Y. Xu and Y. Li are with the