Invariants for LTI Systems with Uncertain Input

Abstract

We propose a new method to derive invariants for LTI systems with uncertain inputs, i.e. systems of the form $\dot x(t) = Ax(t) + Bu(t)$ with state vector x(t) ∈ ℝⁿ and uncertain input u(t) ∈ ℝ^m bounded by u(t) ∈ U ⊆ ℝ^m for all t ≥ 0. Our approach is based on the real canonical form and the resulting invariants are conjunctions of bounds on linear and quadratic forms in the state variables x(t).