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ABSTRACT: This article provides an overview of the circle criterion and its connection with ISS. Classical absolute stability theory and the circle criterion in particular, is concerned with the analysis of a feedback interconnection of Lure type, which consists of a linear system in the forward path and a sector-bounded nonlinearity in the negative feedback path. Classical absolute stability results are revis ited in the context of systems described by differential inclusions and within a framework based on the complex Aizerman conjecture. Contrast with the classical literature that is focused mainly on asymptotic stability of the feedback interconnection, ISS issues are addressed and resolved.
IEEE control systems 09/2011; · 2.49 Impact Factor
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ABSTRACT: For a class of dissipative nonlinear systems, it is shown that an associated dissipation inequality determines an iISS gain. The result can be used to show the convergence of the state trajectory whenever the input signal has bounded energy where the energy function is related to the dissipation inequality.
Decision and Control, 2007 46th IEEE Conference on; 01/2008
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ABSTRACT: The efficacy of proportional, derivative and integral (PID) control for set point regulation and disturbance rejection is investigated in a context of mechanical systems with hysteretic components. Two basic structures are studied: in the first, the hysteretic component resides (internally) in the restoring force action of the system ("hysteretic spring" effects); in the second, the hysteretic component resides (externally) in the input channel (e.g. piezo-electric actuators). In each case, robust conditions on the PID gains, explicitly formulated in terms of system data, are determined under which asymptotic tracking of constant reference signals and rejection of constant disturbance signals is guaranteed.
Decision and Control, 2007 46th IEEE Conference on; 01/2008
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ABSTRACT: For a class of dissipative nonlinear systems, it is shown that an iISS gain can be computed directly from the corresponding supply function. The result is used to prove the convergence to zero of the state whenever the input signal has bounded energy, where the energy functional is determined by the supply function.
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[show abstract]
[hide abstract]
ABSTRACT: The efficacy of proportional, derivative and integral (PID) control for set point regulation and disturbance rejection is investigated in a context of mechanical systems with hysteretic components. Two basic structures are studied: in the first, the hysteretic component resides (internally) in the restoring force action of the system ("hysteretic spring" effects); in the second, the hysteretic component resides (externally) in the input channel (e.g. piezo-electric actuators). In each case, robust conditions on the PID gains, explicitly formulated in terms of system data, are determined under which asymptotic tracking of constant reference signals and rejection of constant disturbance signals is guaranteed.
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[show abstract]
[hide abstract]
ABSTRACT: For a class of dissipative nonlinear systems, it is shown that an associated dissipation inequality determines an iISS gain. The result can be used to show the convergence of the state trajectory whenever the input signal has bounded energy where the energy function is related to the dissipation inequality.
