Event-triggered control for linear time-varying systems using a positive systems approach

Event-Triggered Control for Discrete-Time Systems Using a Positive Systems Approach

“…Second Part: Stability Analysis for Interval Observers ( 15) and ( 22). Using (15), elementary calculations give…”

Event-Triggered Control Under Unknown Input and Unknown Measurement Delays Using Interval Observers

“…This paper continues our development (begun in [7], [8], [9], [10]) of event-triggered control methods for continuous time systems using interval observers (as defined in [2], [12]), positive systems, and the use of matrices of absolute values instead of Euclidean norms. Although our prior eventtriggered works allowed input delays (as well as time-varying coefficients in linear systems and additive uncertainty [10]), they assume that the input delays are known in advance.…”

“…Our novel Hurwitzness condition from Assumption 2 can always be satisfied after a change of coordinates if (A, B) is controllable and if ∆, λ, and ν are small enough. This is done by choosing K so that A + BK has distinct negative eigenvalues, then using a diagonalizing change of coordinates as in [10], so A, B, and K and x are replaced by P −1 AP , P −1 B, KP , and P −1 x respectively for an invertible matrix P . After this coordinate change, H = R H + N H is diagonal and Hurwitz.…”

Event-triggered control for continuous-time linear systems with a delay in the input

“…is that it provides the speed at which the robot is traveling towards the curve that is being tracked (if ∆ * < 0) or away from the curve being tracked (if ∆ * > 0). This contrasts with the undelayed case that was studied in [29], where the corresponding constant ∆ * was required to be nonpositive. Therefore, for this reference trajectory, (1 + ∆ * )/κ is the limit of the distance between the robot and the projection point on the curve being tracked as t → +∞.…”

“…We illustrate our theorem, using a benchmark twodimensional (i.e., planar) curve tracking dynamical system from [22], which we studied in our work [29] that was confined to unelayed cases. While simple (insofar that its only control is a steering control), it will illustrate the value of our approach for compensating any positive constant delay while reducing the computational burden as compared to continuous time controls that are not event-triggered.…”