Paul Hänsch (Informatik 11)
|Title||Invariants for LTI Systems with Uncertain Input|
|Abstract||We present a method to derive invariants for linear time-invariant (LTI) systems with uncertain inputs, i.e. dynamic continuous-time systems of the form dx(t)/dt = Ax(t)+Bu(t) with state vector x(t) in R^n and bounded disturbance input u(t) in R^m.
Our approach is based on the real canonical form. The resulting invariants are conjunctions of bounds on linear and quadratic forms in the state variables x(t), intuitively, they can be seen as intersections of degenerate ellipsoids (i.e. ellipsoids with positive semi-definite shape matrices).
Keywords: Linear time-invariant system, uncertain input, robust invariance, LMI
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