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This paper studies the problem of finite-time H ∞ control for switched nonlinear systems (SNSs), where the powers of chained integrators associated with individual subsystems can be different posit...

In this paper, the adaptive stabilization issue for a class of state-constrained high-order switched nonlinear systems is concerned, where all subsystems are allowed to be unstabilizable. A novel adaptive control scheme is established by exploiting the effective coupling of the technique of adding a power integrator and the method of multiple barrier Lyapunov functions. Explicitly, a group of adaptive controllers and a proper switching law are designed to asymptotically regulate the states of the resulting closed-loop system in a domain and meanwhile guarantee that the violation of the constraints does not happen. Contrary to a common update law constructed for all subsystems in the literature, different update laws for individual subsystems are designed separately to reduce the conservativeness. Moreover, at the switching instants, the connection of two adjacent barrier Lyapunov functions is not be required and even a certain amount of grow is also allowed. Finally, a simulation example is performed to further illustrate the effectiveness of the provided control strategy. (C) 2018 Elsevier Ltd. All rights reserved. National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [61773098, 61773100]; 111 Project, ChinaMinistry of Education, China - 111 Project [B16009] This work was supported by the National Natural Science Foundation of China under Grants 61773098 and 61773100 and the 111 Project, China (B16009).

In this paper, we study stability and L 1 -gain problems for switched positive systems, in which stability for any subsystems do not necessarily requirement. First, the sufficient condition for exponential stability is established. By exploiting the multiple linear co-positive Lyapunov function method, stabilization and L 1 -gain conditions of switched positive systems are proposed. To reduce the switching frequency, a mixed switching strategy is proposed, which is different from traditional state-dependent or time-dependent switching. Then, a set of state-feedback controllers and a mixed switching strategy are dual developed to stabilize the system, and the corresponding linear vector inequalities are examined in terms of linear programming. Furthermore, L 1 -gain is studied as well. Finally, a numerical example is provided to show the validity of the proposed techniques.

This paper addresses the issue of robust stabilisation for a class of state-constrained high-order switched nonlinear systems whose subsystems are allowed to be all unstabilizable. A novel ...

This paper addresses the passivity-based mean square exponential stabilization problem for switched stochastic nonlinear systems. A concept of generalized small-time normobservability is presented and an appropriate test condition is also provided. For pre-given passivity rate and average dwell time, a set of feedback controllers is designed by use of the passivity property. Then, combining with generalized small-time norm-observability, a sufficient condition to guarantee mean square exponential stabilization of a switched stochastic nonlinear system is given. As a special case, the switched stochastic linear system is also discussed. Finally, a numeral example shows the effectiveness of the proposed method.

A framework of regional passivity theory for switched systems is set up using multiple barrier storage functions. The "energy" stored in each subsystem is described by the corresponding individual barrier storage function which is only well defined on an open region associated with regional passivity. The key feature is that the "energy" grows to infinity when the trajectory tends to the region boundary. Firstly, a sufficient condition guaranteeing regional passivity for a switched system is derived under the designed switching law, where all subsystems are not assumed to be regionally passive. Secondly, asymptotic stability can be reached if a switched system is strictly regionally passive or regionally passive plus asymptotic detectability, and meanwhile the system trajectory remains in the corresponding open region. Thirdly, regional passivity is also shown to be preserved under feedback interconnection. Finally, as an application of the theory provided, the stabilization problem for state-constrained strict-feedback switched nonlinear systems is solved, where no subsystem is required to be stabilizable.

In this paper, the passivity-based stabilization problem of a strict-feedback nonlinear system under a proper state-dependent switching law is investigated. Here, the feedback passification problem of each subsystem does not need to be solvable. First, by using the recursive backstepping technique, a sufficient condition under which the closed-loop switched system with designed state feedback controllers is strictly passive from the new input to a designed virtual output is given under a state-dependent switching law. Moreover, the asymptotical stability property of the switched system is achieved by redesigning the introduced new input based on passivity. Finally, a numeral example shows the effectiveness of the proposed method.