Modeling & Simulation
State-space models, system representations, model development, and simulation.
State-Space Models
Linear state space
x_dot = A x + B u, y = C x + D u.
Nonlinear state space
dx/dt = f(x, u), y = g(x, u).
Hybrid systems
Combine continuous dynamics with discrete modes, events, or logic.
Discrete-time state space
Represents sampled dynamics with updates such as x[k+1] = A x[k] + B u[k].
Matrix-exponential discretization
Computes exact linear sampled models under zero-order-hold assumptions.
Discrete models with delays
Represent sensor, actuator, communication, and computation delays by augmentation.
State-command structures
Connect state feedback and observers to tracking commands instead of only regulation.
Integral state augmentation
Adds integrator states or disturbance estimates to remove steady-state errors.
Time-delay systems
Model transport, communication, and computation delays that can destabilize loops.
Saturation & rate limits
Capture actuator limits that strongly affect closed-loop performance.
Stochastic state models
Include process noise, measurement noise, and random disturbances in continuous or discrete time.
Stochastic differential equations
Model continuous-time dynamics driven by random processes or Wiener-process idealizations.