Handbook of Nonlinear Control Systems: Theory, Design, Simulation, and Engineering Applications

Every physical control system is nonlinear underneath its linear approximation, and sooner or later — through actuator saturation, friction, backlash, or an operating range that outgrows a single set of gains — that approximation runs out.

Engineers who have mastered linear control fundamentals often reach a point where the standard toolkit no longer explains what a system is doing. A controller tuned around one operating point starts to underperform, oscillate, or lose stability once the system moves into a regime where nonlinear effects dominate, and the available literature tends to split into two extremes: dense, mathematically abstract graduate texts that assume the reader already understands the material, and applied handbooks that present nonlinear techniques as recipes without the grounding needed to apply them safely.

This handbook builds a complete, sequential path from the mathematical foundations of nonlinear behaviour through a full suite of modern nonlinear control design methods — developed with derivations, worked examples, computational implementation, and real engineering case studies at every stage — so the reader can move from recognising a nonlinear problem to designing, analysing, and deploying a working solution.

Inside, you will learn how to:

• Recognise the sources and classifications of nonlinearity in mechanical and electrical systems, and build accurate first-principles models of them.
• Apply phase-plane analysis, local linearisation, and energy-based stability arguments to determine whether an equilibrium point is genuinely stable, and estimate the region around it where a design remains valid.
• Use geometric tools from differential-equation theory to derive feedback-linearising controllers, and recognise when internal dynamics limit that approach.
• Design and tune sliding-mode, backstepping, adaptive, robust, and passivity-based controllers for systems carrying model uncertainty and external disturbances.
• Combine stabilising and safety-constraining requirements into a single real-time, optimisation-based control law, using barrier-based methods and nonlinear predictive control.
• Build recursive state estimators for systems that cannot be observed with linear techniques, and carry a completed design through discretisation, sampling-rate selection, and real-time deployment on embedded hardware.
• Compare competing nonlinear design philosophies directly, using a structured method-selection guide built around real engineering case studies.

Coverage spans the mathematical and modelling foundations of nonlinear systems, geometric tools for feedback linearisation, sliding-mode and backstepping design, adaptive and robust control under uncertainty, energy-based and passivity-based design, safety-constrained and predictive control, hybrid and networked systems, data-driven and learning-assisted control, and the practical realities of digital implementation. These methods are illustrated through worked case studies, including a robotic manipulator, a magnetic levitation system, a path-following ground vehicle, and a power-electronic converter, along with two integrated, multi-technique capstone design projects.

This handbook is written for senior undergraduates, beginning graduate students, and practising engineers in robotics, aerospace, automotive, biomedical devices, industrial process control, and power electronics who already understand linear control and are ready to work with systems that no longer behave linearly.

Take the next step towards a genuinely comprehensive understanding of nonlinear control — add this handbook to your working library and start building the theory, computation, and design skills that practising control engineers actually use.