The only stable normal forms of affine systems under feedback are linear
Systems & Control Letters
Nonlinear dynamical control systems
Nonlinear dynamical control systems
Nonlinear black-box modeling in system identification: a unified overview
Automatica (Journal of IFAC) - Special issue on trends in system identification
Nonlinear black-box models in system identification: mathematical foundations
Automatica (Journal of IFAC) - Special issue on trends in system identification
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Nonlinear Control Systems
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We consider the problem of topological linearization of smooth (C 驴 or C 驴) control systems, i.e., of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that the local topological linearization implies the local smooth linearization, at generic points. At arbitrary points, it implies the local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology.