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In Part I of this paper, we introduced the notion of L??-vanishment and established several kinds of characterizations of this notion. Based on this notion, L?? low gain feedback was reconsidered and a systematic approach to L?? low gain feedback design was proposed. In this second part of the paper, we consider the parallel notion of L2-vanishment. We establish several characterizations of the L2...
In a multi-agent system (MAS), the agents are often considered to be autonomous entities, such as robots or software programs, each under the influence of a local rule, representing its interaction with other agents. Over the past few years, most research in the study of discrete-time MAS's concentrates on linear local rules. However, local interactions between agents are more likely to be governed...
This paper considers the design of decentralized controllers for large-scale linear systems subject to multi-layer nested saturation. The design of decentralized state feedback laws that result in large domains of attraction are formulated as optimization problems with LMI and BMI constraints. Numerical algorithms are developed to solve these problems.
Low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initially proposed to achieve semi-global stabilization of linear systems subject to input saturation. It was then combined with high gain feedback in different ways for solving various control problems. The resulting feedback...
This paper considers the stabilization problem for a port-controlled Hamiltonian system subject to actuator saturation and input additive external disturbances. Conditions are identified under which a static output feedback law would achieve global asymptotic stabilization. Under some additional growth conditions on the nonlinear functions involved in the system, the same feedback law would also achieve...
Recently, we developed a structural decomposition for multiple input multiple output nonlinear systems that are affine in control but otherwise general. This structural decomposition simplifies the conventional backstepping design and allows a new backstepping design procedure that is able to stabilize some systems on which the conventional backstepping is not applicable. In this paper we further...
This paper studies some properties of the recently developed parametric Lyapunov equation based low gain feedback design method. As applications of these new properties, alternative and simpler solutions are proposed to the (global) stabilization problem for a class of linear systems with input delay and the semi-global stabilization problem when the systems are in addition subject to actuator saturation...
This paper extends the recent results of [8] on semi-global stabilisation of a class of minimum-phase nonlinear systems via linear state feedback. The class of minimum-phase nonlinear systems considered in this paper subsume those of [8]. More specifically, we show, by explicit construction of the control laws, that a cascade of linear stabilisable and nonlinear asymptotically stable subsystems is...
In this paper we study global stabilisation, using output feedback, of single-input-single-output nonlinear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy. The nominal systems are assumed to be smooth, have a certain strong relative degree and be of minimum-phase. Model uncertainties are dealt with either by restricting them to be structured...
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