Sequential predictors for delay-compensating feedback stabilization of bilinear systems with uncertainties

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

“…We found these assumptions on the delay to be suitable for practice, because for instance, one can first apply delay estimation methods such as the notable work [13] or experiments for delay estimation. Also, in the surface marine robotic, power electronics, and other applications that we encountered, the delays are typically constant and pointwise; see, e.g., [4], and see [27] and [38] for sequential predictor methods under time-varying delays but no event triggering, which we conjecture can be extended to event triggering using the approach in the present work, because the present work uses the constantness of the delay primarily in the chain predictor construction.…”

“…On the other hand, many systems have input delays, which frequently arise from transport and delays in sensors; see, e.g., [5], [6], [7], [8], [9], [10], [11], and [30]. Even small input delays can have detrimental effects, so it can be essential to take them into account; see, e.g., [4] for a gridtied inverter dynamics that is destabilized by a delay of τ = 0.001. To cope with input delays, several stabilization techniques exist in the frequency and time domains, in-Supported by NSF Grants 1711299 and 2009659.…”

Feedback control of isolation and contact for SIQR epidemic model via strict Lyapunov function

“…The parameter ρ(t) not only describes the amount of vaccine administration in the society, but also the reciprocal of the average time to acquire immunity. Due to the non-negativity of the parameters, the non-negative orthant [0, ∞) 4 is a forwardly invariant set for (1). In other words, each state component of (1) stays nonnegative for all t ≥ 0 if the initial state for (1) is in [0, ∞) 4 .…”

“…for (1). Irrespective of the control inputs u V , u I , and u C , the set D is forwardly invariant for (1).…”

Strict Lyapunov functions and feedback controls for SIR models with quarantine and vaccination

“…Our stepwise construction of ISS Lyapunov functions directly provided reasonable controllers that are independent of downstream populations and allowed us to concentrate only on susceptible and infected populations in achieving the ISS guarantee involving all four populations. In future work, we will study the effects of input delays [4,13,22] in our feedback controls, as well as delay compensation based on exact predictors, chain predictors [3,5], or other dynamic extensions [25]. with k 1 defined in (11).…”