Controllability and observability of a class of linear, time-invariant systems with interval plants

Abstract

We establish necessary and sufficient conditions for the controllability of single input/multi output linear time-invariant systems with interval plants, and for the observability of multi input/single output linear time-invariant systems with interval plants. In arriving at our results, we determine allowable plant uncertainty bounds for controllability and observability.To demonstrate the applicability of our results, we consider two specific examples.

Stability of stochastic interval systems with time delays

“…Hence, it is clear that satisfaction of condition (12) implies satisfaction of condition (14). This completes the proof.…”

“…Therefore, in order to prove Theorem 2 we need only demonstrate that (12) guarantees (14). Firstly, we note that…”

“…This type of system has been examined in several papers, for instance, Han and Lee [2] and Wang et al [13,14]. Similar systems which incorporate time delays have also been studied, for example, Sun et al [12].…”

Ellipsoidal Set-Membership State Estimation for Multi-Output Systems with Interval Uncertainties

“…, and F have the appropriate dimensions, with the pair (C δ , A δ ) detectable (see [29] for the detectability of linear time invariant systems with interval plants). An additional assumption is to consider a quadratically stable interval matrix [A] for a common quadratic Lyapunov function.…”