A robust controller maintains stability and performance despite:
In linear control, robustness is quantified by gain/phase margins. In nonlinear control, the language changes to input-to-state stability (ISS) , Lyapunov redesign, and sliding modes. In linear control, robustness is quantified by gain/phase
If you take away one practical technique from this book, it’s Sliding Mode Control (also called Variable Structure Control). In linear control
Imagine you have a car on ice. You want it to track a line. Linear control might push gently. Sliding mode control? It slams the wheel left and right at high frequency to force the car to "slide" along the desired trajectory. Mathematically, you design a surface ( s(x) = 0 ) and then enforce ( \dots = -k \cdot \textsign(s) ). In linear control, robustness is quantified by gain/phase
The beauty: Once on the surface, the system is insensitive to matched uncertainties and disturbances. The ugly: "Chattering"—high-frequency switching that can excite unmodeled dynamics (or break your actuator).
The book doesn't just present sliding mode; it shows you how to smooth it (boundary layers, saturation functions) for real-world implementation.
Real-time robust nonlinear control requires: