This article is concerned with$L_{-}$fault detection functional observer design for the switched positive systems (SPSs) with unknown external input under mode-dependent minimum dwell time (MDMDT) constraint. First, a necessary and sufficient condition is presented, such that the designed p-order functional observer provides a positive estimation with an$L_{-}$fault sensitivity performance. Then, a new discretized linear co-positive Lyapunov function method is proposed to derive the asymptotic tracking condition of the$L_{-}$fault detection functional observer under the MDMDT constraint. Further, the matrix decomposition technology is applied to solve the bilinear inequality problem in the observer gain matrix design, and an effective mode-dependent piece-wise design scheme of the$L_{-}$fault detection functional observer in the linear programming form is proposed. The designed$L_{-}$functional observer is not only sensitive to fault but also robust against any form of unknown input. The results are also extended to the cases of mode-dependent constant dwell time (MDCDT) constraint, mode-independent dwell time constraint, and non-SPSs. Finally, the proposed method is illustrated in detail by constructing a fault detection observer for a traffic signal system. Simulation results verify the effectiveness of the theoretical results.

This paper studies the relative-position-based reference-frame-free formation control in the plane for discrete-time multiagent systems under both measurement and communication noises. To achieve the desired formation, a robust distributed orientation estimate algorithm and a robust distributed formation control law are designed. The main idea of our method is to use the historical measurement information to get unbiased estimates and use the stochastic approximation method to inhibit the noise. Under mild assumptions on the measurement/communication noises and agents' initial orientation angles, we show that a common reference frame can be asymptotically shared by all agents and the desired formation can be asymptotically stabilized almost surely under the designed distributed control law, if and only if the magnitude of the bearing measurement noise is less than ( π / 4) , the communication and distance sensing topology is rooted and the corresponding bearing sensing topology is connected. Simulations are conducted to verify the correctness and effectiveness of our orientation estimate algorithm and formation control law.

This paper considers the cooperative control problem of second-order agents formation tracking a set of given curves on spheres when each agent suffers an unknown spatiotem-poral flowfield. The flowfield under consideration is composed of three known base vectors and the unknown corresponding coefficients. A novel coordinated adaptive estimator is proposed to estimate the unknown flow coefficients based on the neighbor to neighbor information. Adaptive backstepping, the geometric extension design and consensus are combined to design the robust spherical formation tracking control law. The effectiveness of the analytical results is verified by numerical simulations.

This paper considers the problem of directing a family of underactuated ships to formation tracking a set of closed orbits and achieve attitude synchronization. It shows that our previous concentric compression design is useful to the coordinated motion of underactuated ships. The condition that the total linear speed of each ship is greater than zero is ensured by introducing a potential function. Asymptotical stabilization is proved when the inter-ship communication topology is bidirectional. The theoretical result is proved by a numerical example.

This paper addresses the problem of the stability of congestion control for networks with heterogeneous round-trip communication delays. We present a frequency-domain approach to this problem. The approach is based on the analysis of the clockwise property of system transfer functions, generalized Nyquist stability criterion, and a recent lemma of Vinnicombe. We point out that a prerequisite for establishing decentralized stability criteria for distributed congestion control is that the Nyquist plots of time-delayed transfer functions corresponding to price (rate) dynamics at links (sources) satisfy clockwise property in certain frequency intervals. Based on the detailed investigation of global geometric properties of the frequency response of price dynamics at links, we derive sufficient conditions for the local asymptotic stability of a kind of the second-order active queue management algorithm-REM algorithm. A simple design procedure is also proposed for guaranteeing the asymptotic stability of the control algorithm.