Isometric Torque Control for Neuromuscular Electrical Stimulation With Time-Varying Input Delay

Sequential Predictors for Linear Time-Varying Systems with Delays in the Vector Field and in the Input

“…interconnected with (13) and (17). Since (16) and (18) express σ and ζ as linear combinations of the components of (z a , z b ), and the (z a , z b ) subsystem of (19) is uniformly globally exponentially stable to 0, it follows from Assumption 1 and the linearity of u s in x that (19) is uniformly globally exponentially stable to 0, which proves the theorem.…”

“…,z pk . Using the uniform global exponential stability of the dynamics (13) for z a , the telescoping sum (16), and the exponential input-to-state stability of (14) with respect to δ, it follows that the dynamics for (z a , z b ) = (z 1 , . .…”

“…z pk−s t + sτ p (18) for all t ≥ 0 (using a telescoping sum argument as we did to obtain (16)). Then the dynamics for the combined variable (x(t), z 1 (t), .…”

“…Feedback stabilization can be challenging from the theory side, and also has many engineering motivations. See, e.g., the work [16], and [4], [17], and [21] which provide useful surveys of delay compensating control. The usual prediction approach eliminates feedback delays, by replacing the delayed states in the feedback by predicted values.…”

New prediction approach for stabilizing time-varying systems under time-varying input delay

“…Our work is motivated by the ubiquity of input delays across engineering, and the challenges that can occur when building delay tolerant controls, if one applies traditional methods that have distributed terms. See, e.g., [4] and [17], and [6], [15], [18] for electromechanical input delays in muscle response in neuromuscular electrical stimulation (or NMES). For constant coefficient linear systems, it often suffices to use linear matrix inequalities (or LMIs) to build delay tolerant controls, but many important linear systems are time-varying.…”