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For a discrete-time linear system that has an open-loop pole outside the unit circle and is subject to actuator saturation, global asymptotic stabilization cannot be achieved. As a consequence, a discrete-time multi-agent system containing such an actuator saturating agent can only reach regional consensus, that is, the consensus can be achieved only if the initial state of each agent resides in a...
This paper proposes an asymmetric Lyapunov function approach to the estimation of the domain of attraction for a linear system subject to asymmetric actuator saturation. Depending on the sign of each of the m inputs, the input space is divided into 2m regions. In each region, the linear system with asymmetrically saturated inputs can be expressed as a linear system with symmetric deadzones. A quadratic...
This paper revisits the problem of estimating the domain of attraction for systems with saturation nonlinearities. We divide the input space into several regions. In one of these regions, none of the inputs saturate. In each of the remaining regions, there is a unique input that saturates everywhere with the time-derivative of its saturated signal being zero. These special properties of the inputs...
This paper studies local control of discrete-time periodic linear systems subject to input saturation by using the multi-step periodic invariant set approach. Multi-step periodic invariant set refers to a set from which all trajectories will enter a periodic invariant set after finite steps, remain there forever, and eventually converge to the origin as time approaches infinity. A couple of problems...
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