Index abs command, 140, 484 Absolutely summable impulse response sequences, 91, 286, 288 Accuracy, in digital control, 2 acker command, 376 Ackermann's formula, 341-344 Actuators, 2-3 furnace model, 113-114 noise damage, 471 saturation nonlinearity, 472-475 tank control system, 467 ADCs (analog-to-digital converters), 3-6, 55 models, 55-56 quantization errors, 464-466 selecting, 460-461 stable range, 103-104 transfer functions, 62-70 Addition of matrices, 502 Adjoint matrices, 509 Aircraft turbojet engine, 4-5 Algebraic loops, 477 Algebraic Lyapunov equation, 400 Algebraic multiplicity of eigenvalues, 512 Aliasing, 462-464, 466-467 Allocation, pole, 337 Analog control system design, 123 computer exercises, 159-160 design specifications and gain variation, 128-131 Angle of arrival, in root locus method, 124 Angle of departure, on root locus method, 124 Angles bilinear transformations, 184 contours, 105-106 root locus method, 124, 126 Anthropomorphic manipulators state­space equations, 235-236 torque vectors, 417-418 Anti-windup techniques, 473 Antialiasing filters, 462-464, 466-467 Armature-controlled DC motors full-order observers, 357-358, 365-366, 368-369 gain vector, 344 PID controllers, 151-152 pole assignment, 372-374 reduced-order observers, 361-362, 367-368 root locus method, 133-134 state equations, 242-243 z-domain transfer function, 68-70 Assignment, pole, 337, 370-374 Asymptote angles, in root locus method, 126 Asymptotic stability, 88, 283-285 with BIBO stability, 289 conditions, 90-91 equilibrium points, 282-283, 428-430 global, 429 LTI systems, 90, 93