This article considers the finite-frequency (FF) $H_{2}$ - $H_{\infty }$ composite control problem for continuous singularly perturbed systems. To address the performance requirements in the low- and high-frequency ranges, the FF $H_{2}$ and $H_{\infty }$ norms are used to impose on the performance of the slow and fast subsystems, respectively. The FF $H_{2}$ control of the slow subsystem is analyzed using the FF Gramian matrix method. While the FF $H_{\infty }$ control of the fast subsystem is studied by using the Generalized Kalman-Yakubovič-Popov Lemma. Subsequently, an $H_{2}$ - $H_{\infty }$ composite controller for the singularly perturbed system is developed. Finally, two simulation examples involving an armature control direct-current motor system are demonstrated to verify the effectiveness and superiority of the proposed control scheme.

This article introduces an innovative approach to tackle the consensus issue for positive multiagent systems (MASs) with input nonlinearities. By analyzing a differential equation model of MASs with sector-bounded nonlinearity, positivity conditions are derived. Furthermore, a distributed state-feedback control protocol is applied to achieve consensus and simultaneously to preserve positivity. An iterative algorithm is used to compute a consensus controller gain. The saturation nonlinearity and its approximated form are also considered. Finally, the effectiveness of proposed method is verified through numerical examples. The findings of this study can potentially contribute to developing control strategies for MASs with nonlinear input dynamics.

This work addresses the output reachable set-based leader-following consensus problem, focusing on a group of positive agents over directed dwell-time switching networks. Two types of non-negative disturbances, namely, 1)$L_{1}$-norm bounded disturbances and 2)$L_{\infty,1}$-norm bounded disturbances are studied. Meanwhile, a class of directed dwell-time switching networks for modeling the communication protocol of positive agents is investigated. To deal with the presence of disturbances, an output-feedback control protocol is developed to achieve a robust consensus with positivity preserved based on the output reachable set. By exploiting the positive characteristics, switched linear copositive Lyapunov functions are adopted to establish output reachable set-based consensus conditions. These conditions can facilitate the control protocol design by solving a bilinear programming problem, and also generate hyperpyramidal regions to confine the output consensus error. A particle swarm optimization-based (PSO-based) algorithm is applied to compute the controller gains and optimize the volume of the hyperpyramids. The proposed methods are verified by the presented numerical case studies.

This work addresses the problem of reachable set-based consensus for positive multiagent systems affected by typical classes of bounded disturbances. In the presence of disturbances, a reachable set-based consensus with positivity preservation is proposed to ensure that the state of the closed-loop system remains positive while enclosing the reachable set of the defined consensus error with an ellipsoidal bounding region. Sufficient conditions are established to achieve the reachable set-based positive consensus under the energy-bounded or peak-bounded disturbance input. Equivalent design conditions are provided, for which a heuristic algorithm is proposed for computing and optimizing the bounding region. Simulations are conducted to validate the obtained results.

The bounded stability problem of linear mixed quantum-classical feedback control systems with time delays is investigated in this paper. The whole feedback system is composed of a quantum plant, a classical controller, and some interconnection devices. Two classes of feedback delays in the feedback loop are considered: constant delays and time-varying delays. The stability of the closed-loop systems under these two classes of time delays is analyzed by constructing different Lyapunov-Krasovskii functions and the corresponding stability criteria are derived, respectively. In particular, a weighting matrix is introduced into stability analysis and the obtained stability results are less conservative than relevant results for this class of quantum systems.