Robust stability of input-output systems with initial conditions. (English) Zbl 1317.93128
Summary: We consider the development of a general nonlinear input-output theory which encompasses systems with initial conditions. Systems are defined in a set theoretic manner from input-output pairs on a doubly infinite time axis, and a general construction of the initial conditions is given in terms of an equivalence class of trajectories on the negative time axis. Input-output operators are then defined for given initial conditions, and a suitable notion of input-output stability on the positive time axis with initial conditions is given. This notion of stability is closely related to the ISS/IOS concepts of Sontag. A fundamental robust stability theorem is derived which represents a generalization of the input-output operator robust stability theorem of Georgiou and Smith, to include the case of initial conditions. This includes a suitable generalization of the nonlinear gap metric. Some applications are given to show the utility of the robust stability theorem.
MSC:
| 93C10 | Nonlinear systems in control theory |
| 93D09 | Robust stability |
| 93D25 | Input-output approaches in control theory |
| 93D15 | Stabilization of systems by feedback |
| 93D20 | Asymptotic stability in control theory |
Keywords:
nonlinear systems; robust stability; gap metric; feedback connection; small-gain-like stability theorem; iss/iosReferences:
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