For the Laplace transform used in the analysis of linear systems see:-

*Transient Response Introduction**1 pole Step Response**1 pole Ramp Response**1 pole 1 zero Step Response**2 Real poles Impulse Response**2 CC poles Impulse Response**2 Real poles Step Response**2 CC poles Step Response**2 poles Ramp Response**2 poles Sine Response**2 Real poles Modified Step Response**2 Real poles Modified 2 Step Response**2 Real poles 1 Real Zero Step Response**3 Real poles Step Response**3 Real poles Type 0 Impulse Response**3 Real poles Type 1 Impulse Response**3 Real poles 1 Zero Step Response**3 Real poles 0, 1, 2 Zeros Step Response**1 Real 2 CC poles Step and Impulse Response**4 Real poles Step Response**2 x Complex Conjugate Poles Step Response**1, 2, 3, 4 Real poles Sine Response**3 Real poles Step Response and Closed Loop Poles**Frequency Analysis Introduction**S Plane and Frequency Response**Bode Plot, Single Pole Zero Factors**Bode Plot, Quadratic Pole Zero Factors**Quick look at Bode Plots.**Bode Plot, 1 Pole, 1 Zero Factors**Nyquist Plot, 1, 2, 3 Real Poles**Bode Plot, 2 Real Poles, 1 Zero**Nyquist Plot, 2 Real Poles, 1 Zero**Bode Plot, 3 Real Poles**Bode Plot, 3rd order Polynomial**Bode Plot, 3 Real Poles, 1 Zero**Nyquist Plot, 3 Real Poles, 3 Real Poles, 1 Zero**Bode Plot, 3 Real Poles, 2 Complex Conjugate Zeros**Bode Plot, 3 Real Poles, Closed Loop Response**Nyquist Plot, 3 Real Poles, Closed Loop Response**Bode Plot, 3 Real Poles, Phase and Gain Margins**Nyquist Plot, 3 Real Poles, Phase and Gain Margins**Bode Plot, 1 Real Pole, 2 Complex Conjugate Poles**Nyquist Plot, 1 Real Pole, 2 Complex Conjugate Poles**Bode Plot, 4 Real Poles**Nyquist Plot, 4, 3 Real Poles**Bode Plot, 4 Real Poles, 2 Complex Conjugate Zeros**Nyquist Plot, 4 Real Poles, 2 Complex Conjugate Zeros**Bode Plot, 4th Order Polynomial**Bode Plot, 5 Real Poles**Nyquist Plot, 5 Real Poles**Routh Hurwitz Introduction**Routh Hurwitz, 3 Real Poles**Routh Hurwitz, 3 Real Poles, 2 Complex Conjugate Zeros**Routh Hurwitz, 3rd Order Polynomial**Routh Hurwitz, 4 Real Poles**Routh Hurwitz, 4 Real Poles, 2 Complex Conjugate Zeros**Routh Hurwitz, 4th Order Polynomial**Routh Hurwitz, 5 Real Poles**Routh Hurwitz, 5th Order Polynomial**Routh Hurwitz, 3 Real Poles and closed loop poles**Routh Hurwitz, 3rd Poly and closed loop poles**Routh Hurwitz, 4th Poly and closed loop poles**Root Locus Introduction**Angle Condition, Quick look at Root Locus for Pole Zero Configurations**Angle Condition, 1 Real Pole, 1 Real zero**Angle Condition, 2 Real Poles**Angle Condition, 2 Real Poles, Magnitude and Phase Surface Plots**Angle Condition, 2 Real Poles, 1 Real zero**Angle Condition, 3 Real Poles, type 0 and 1**Angle Condition, 3 Real Poles and root locus**Angle Condition, 3rd order Polynomial**Angle Condition, 3 Real Poles, Magnitude and Phase Surface Plots**Angle Condition, 3 Real Poles, 1 Real Zero**Angle Condition, 3 Real Poles, 1 Real Zero, Root Locus**Angle Condition, 3 Real Poles, 2 Real Zeros**Angle Condition, 3 Real Poles, 2 Complex Conjugate Zeros**Angle Condition, 1 Real Pole, 2 Complex Conjugate Poles, 2 Real Zeros**Angle Condition, 1 Real Pole, 2 Complex Conjugate Poles, 2 Complex Conjugate Zeros**Angle Condition, 4 Real Poles**Angle Condition, 2 Real Poles, 2 Complex Conjugate Poles**Angle Condition, 2 x 2 Complex Conjugate Poles**Angle Condition, 4 Real Poles, 1 real Zero**Angle Condition, 4 Real Poles, 2 real Zeros**Angle Condition, 2 Real Poles, 2 Complex Conjugate Poles, 1 real Zero**Angle Condition, 4 Real Poles, 2 Complex Conjugate Zeros**Angle Condition, 2 x 2 Complex Conjugate Poles, 2 Complex Conjugate Zeros**Angle Condition, 4th Order Polynomial**Angle Condition, 5 Real Poles**Angle Condition, 5 Real Poles, 1Real Zero.**Angle Condition, 5 Real Poles, 2 Real Zeros.**Angle Condition, 5 Real Poles, 2 Complex Conjugate Zeros.**Angle Condition, 3 Real Poles, 2 Complex Conjugate Poles, 2 Complex Conjugate Zeros**Angle Condition, 1 Real Poles, 2 x 2 Complex Conjugate Poles, 2 Complex Conjugate Zeros**Angle Condition, 5th Order Polynomial**Magnitude Condition, 3 Real Poles**Magnitude Condition, 3 Real Poles, 1 Real Zero**Magnitude Condition, 3 Real Poles, 1 Real Zero, Contour Plot**Distance Velocity Lag and Nonminimum Phase introduction**Distance Velocity Lag, Transient Response and Bode Plot**Distance Velocity Lag, Transient Response and Nyquist Plot**Distance Velocity Lag, Transient Response and Root Locus**NonMinimum Phase, Transient Response**NonMinimum Phase, Bode Plot**NonMinimum Phase, Root Locus**Compensator Introduction**Compensator Controller Comparison**Second Order Phase Lead Compensator**Second Order Phase Lag Compensator**Second Order Phase Lag Compensator, Root Locus**Second Order Phase Lag Lead Compensator**Second Order Lead, Lag and LagLead Ramp Response.**Second Order LagLead compensator, Root Locus.**Third Order Phase Lead Compensator.**Third Order Phase Lag Compensator.**Third Order Phase Lag Lead Compensator.**Third Order Lead, Lag and LagLead Ramp Response.**Comparison of Compensators for 2 poles.**Comparison of Lead Compensator and PD Control.**Comparison of Lag Compensator and PI Control.**Comparison of Compensators for 3 poles.**Introduction**P Control 1st, 2nd, 3rd and 4th order**First Order P, P + I Control, Step Response**First Order P, P + I Control, Ramp Response**First Order P, P + I Control, Disturbance**First Order P, P + I Control, Bode Plot**First Order P, P + I Control, Nyquist Plot**First Order P + I Control, Root Locus**Second Order P + D Control, Step Response**Second Order P + D Control, Ramp Response**Second Order P + D Control, Disturbance Response**Second Order P + D Control, Bode Plot**Second Order P + D Control, Nyquist Plot**Second Order P + D Control, Root Locus**Second Order Tachometer Control(Velocity Feedback), Step Response**Second Order Tachometer Control, Ramp Response**Second Order Tachometer Control, Bode Plot**Second Order PID Control, Step Response, Bode, Nyquist, Rootlocus, Routh Hurwitz**Second Order PID Control, Step response.**Second Order PID Control, Controller Outputs**Second Order PI, PD, PID Control, Ramp Response**Second Order PI, PD, PID Control, Parabolic Response**Second Order PI, PD, PID Control, Disturbance Response**Second Order PI, PD, PID Control, Bode Plot**Second Order PI, PD, PID Control, Nyquist Plot**Second Order PI, PD, PID Control, Root Locus**Second Order PID Control, Root Locus**Third Order PD Control**Third Order PD Control, Bode Plot**Third Order PD Control, Nyquist Plot**Third Order PD Control, Root Locus**Third Order PID Control**Third Order PID Control, Bode Plot**Third Order PID Control, Nyquist Plot**Third Order PID Control, Root Locus**Second Order I-PD Control**Optimal Control Introduction.**Optimal Control P, PD Control.**Optimal Control PI Control.**Optimal Control PID Control.**Optimal Control Lead Compensator.**Optimal Control Lag Compensator.**Optimal Control 2 Step input.**Optimal Control Ramp to Step input.**Optimal Control Cos to Step input.**Optimal Control Exponential input.**State Vector Introduction.**Second Order, Product State Vector, Step Response and Bode Plot**Second Order, Partial Fraction State Vector, Step Response and Bode Plot**Second Order, Companion Matrix State Vector, Step Response and Bode Plot**Second Order, Product State Vector, Pole Placement**Second Order, Companion Matrix State Vector, Pole Placement**Third Order, Product State Vector, Step Response and Bode Plot**Third Order, Product State Vector, Sine Response and Bode Plot**Third Order, Partial Fraction State Vector, Step Response and Bode Plot**Third Order, Companion Matrix State Vector, Step Response and Bode Plot**Third Order, Companion Matrix State Vector, Sine Response and Bode Plot**Third Order, Product State Vector, Pole Placement Step Response and Bode Plot**Third Order, Product State Vector, Pole Placement Step Response and Root Locus**Third Order, Companion Matrix State Vector, Pole Placement**Third Order 3RP1Z, Companion Matrix State Vector, Step Response and Bode Plot**Multi Input, Introduction**Multi Input, Root Locus, Step and Sine Response**Nonlinear Introduction.**First Order, On Off Control, Step Response and Bode Plot**Second Order, On Off Control, Step Response and Bode Plot**Second, Third Order, Saturation, Step Response and Bode Plot**Second Order, Nonlinear Oscillator, Frequency and Amplitude dependence.**Second order Cubic Nonlinearity, Step Response**Third order Cubic Nonlinearity, Step, Sine Response**Second Order, Dead Band, Step Response and Bode Plot**Second Order, Back Lash and Describing Function**Second Order, Van Der Pol Limit Cycles**Second Order, Nonlinear Pendulum, Chaotic Response**Second Order 2RP, Phase Plane**Second Order 2RP1Z, Phase Plane**Third Order 3Rp, Phase Plane**First Order Type Zero, P Control Step and Ramp response**First Order Type Zero, P Control Sine and Impulse response**First Order Type One, P Control Step and Ramp response**First Order Type One, P Control Sine and Impulse response**First Order Type Zero, PI Control Closed loop Pole Zero locations.**First Order Type Zero, PI Control Step and Ramp response, Z Transfer Function**First Order Type Zero, PI Control Step and Ramp response, Finite Difference Trapezoidal Approximation**First Order Type Zero, PI Control Frequency response, Z Transfer Function and Finite Difference Approximation**Second Order Type Zero, P Control Step Response and Bode Plot**Second Order Type Zero, P Control Step Response and Root Locus**Third Order Type Zero, P Control Step Response and Bode Plot**Third Order Type Zero, P Control Step Response and Root Locus**Second Order Type Zero, PD Control Root Locus**Second Order Type Zero, PD Control Step and Ramp response, Z Transfer Function**Second Order Type Zero, PD Control Step and Frequency response, Z Transfer Function**Second Order Type Zero, PD Control Step Response and Root Locus, Z Transfer Function**Second Order Type Zero, PD Control Step and Ramp response, Finite Difference Approximation**Second Order Type Zero, PD Control Step and Frequency response, Finite Difference Approximation**Second Order Type Zero, PD Control Step Response and Root Locus, Finite Difference Approximation**Second Order Type Zero, PID Control Step and Ramp response, Finite Difference Approximation**Second Order Type Zero, PID Control Step Response and Bode Plot, Finite Difference Approximation**Second Order Type Zero, PID Control Step Response and Root Locus, Finite Difference Approximation**Second Order Type Zero, PID Control Root Locus**Second Order Type One, Lead Compensator Ramp response, Finite Difference Approximation**Second Order Type One, Lead Compensator Step Response and Bode Plot, Finite Difference Approximation**Second Order Type One, Lead Compensator Step Response and Root Locus, Finite Difference Approximation**Second Order Type One, Lag Compensator Ramp response, Finite Difference Approximation**Second Order Type One, Lag Compensator Step Response and Bode Plot, Finite Difference Approximation**Second Order Type One, Lag Compensator Step Response and Root Locus, Finite Difference Approximation**Second Order Type One, LagLead Compensator Ramp response, Finite Difference Approximation**Second Order Type One, LagLead Compensator Step Response and Bode Plot, Finite Difference Approximation**Second Order Type One, LagLead Compensator Step Response and Root Locus, Finite Difference Approximation*

For the Z transform used in the analysis of sampled systems see:-