Stabilization of linear impulsive systems under dwell-time constraints: Interval observer-based framework

Abstract

The problem of interval observer design is studied for a class of linear impulsive systems. Ranged and minimum dwell-time constraints are considered under detectability assumption. The first contribution of this paper lies in designing interval observers for linear impulsive systems under ranged and minimum dwelltime constraints, and investigating positivity of the estimation error dynamics in addition to stability. Several observers are designed oriented on different conditions of positivity and stability for estimation error dynamics. The boundedness of the estimation error (input-to-state stability property) and the observer stability conditions are stated as infinite-dimensional linear programming problems. Next, an output stabilizing feedback design problem is discussed, where the stability is checked using linear matrix inequalities (LMIs). Efficiency of the proposed approach is demonstrated by computer simulations for a commercial electric vehicle equipped with a low power range extender fuel cell, a bouncing ball, an academic linear impulsive system and for Fault Detection and Isolation (FDI) and Fault-Tolerant Control (FTC) of a power split device with clutch for heavy-duty military vehicles.

Interval functional observers for time‐delay systems with additive disturbances

“…In this article, this assumption is replaced by assumption (A 1 ) where z(t) ∈  r ∞ . There are works in the literature dealing with systems subject to additive output disturbance vector v(t) (see, eg, References 11,[16][17][18]. In those works, assumption (A 2 ) is assumed to be satisfied which implies that v(t) is bounded with a known bound v > 0.…”

Interval Observers for Secure Estimation in Cyber-Physical Systems

“…Assumption 3 is essential for the interval estimation approach, but it is rather restrictive. It can be relaxed using a coordinate transformation [16], [18], which is omitted here for brevity and simplicity of notation. If the monitoring system does not take into account the presence of an attack, it believes the system model to be (1), whereas it measures in fact y a from (2) or (4).…”

“…However, this technique can be difficult to apply in practice to design Fault Detection and Isolation (FDI) systems, where simpler observers with tunable gains are more common. On the other hand, interval observers [16]- [18], which are a subclass of setmembership estimators, take into account the measurements by using observer gains explicitly, and have become one of the most common approach for FDI during the last decade [15]. In this paper, we focus on secure estimation under stealthy attacks with interval observers.…”

Interval Observer-based Feedback Control for Rehabilitation in Tremor

“…For these parameters, we assume that the exact values are not available, only bounds are given. Following [18], [19], first, we evaluate the state signal bounds, assuming that the control signal is given. Next, we use these bounds to design a stabilizing control law for the observer's system.…”