## Discrete-time Control SystemsThe new edition of this comprehensive digital controls book integrates MATLAB throughout the book. The book has also increased inflexibility and reader friendliness through the streamlining of coverage in Chapters 6 & 7 (controllability, pole placement and observability, and optimal control). The previous edition ISBN is: 0-13-216102-8. |

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assume asymptotically stable block diagram Bode diagram characteristic equation characteristic polynomial closed-loop poles closed-loop pulse transfer completely state controllable Consider the system continuous-time system control signal deadbeat response deﬁned determined digital control system discrete-time control system discrete-time system eigenvalues eigenvectors feedback gain matrix ﬁrst first-order hold frequency given by Equation Gx(k Hence Hu(k inverse z transform Jordan canonical form Kronecker delta last equation lead compensator Liapunov function linear time-invariant MATLAB MATLAB Program matrix G method minimal polynomial n x n n-vector Note open-loop optimal control output equation performance index PID controller plane pole placement poles and zeros positive definite Problem pulse transfer function Referring to Equation root loci sampler sampling instants sampling period sequence shown in Figure Solution state-space representation static velocity error steady-state error system defined theorem unit circle unit-ramp response unit-step input unit-step response variables velocity error constant x(kT y(kT zero-order hold