What are the 4 main categories of hybrid system?
Hybrid systems are typically categorized into four widely recognized families: switched systems, hybrid automata, piecewise affine (or piecewise linear) systems, and stochastic hybrid systems. This taxonomy helps engineers select the right modeling, analysis, and control tools for complex systems that blend continuous dynamics with discrete decisions.
In practice, researchers distinguish these categories by how discrete modes interact with continuous evolution. Some models emphasize mode switching driven by timing or state conditions (switched systems); others formalize the combination of continuous flows with discrete transitions using automata-based frameworks (hybrid automata); yet others approximate nonlinear behavior with regional, linear pieces (piecewise affine systems); and a final group explicitly integrates randomness and uncertainty into both discrete transitions and continuous dynamics (stochastic hybrid systems).
Categories at a glance
Below is a compact taxonomy commonly cited in control theory and applications. Each item captures a core modeling approach used across engineering disciplines.
- Switched systems: The system follows one of several continuous-time dynamical models, with mode changes governed by a switching signal that may be time-driven or state-driven.
- Hybrid automata and hybrid dynamical systems: Continuous evolution occurs within discrete modes, and transitions between modes follow a formal automaton or state machine, enabling precise modeling and verification.
- Piecewise affine (or piecewise linear) systems: The state-space is partitioned into regions, each with its own affine (or linear) dynamics, allowing nonlinear behavior to be captured piecewise.
- Stochastic or probabilistic hybrid systems: Randomness is integrated into either the discrete transitions, the continuous dynamics, or both, using frameworks like Markov models or stochastic differential equations.
These categories cover a broad spectrum of real-world systems encountered in robotics, energy systems, manufacturing, and cyber-physical platforms. Many practical models combine characteristics from multiple categories, requiring hybrid analysis and design tools that can handle mixed behaviors.
Switched systems
Switched systems are defined by a family of continuous-time subsystems and a switching rule that selects which subsystem is active at any given time. Stability and performance often hinge on dwell-time conditions and the existence of common or multiple Lyapunov functions to guarantee reliable behavior under switching.
Hybrid automata and hybrid dynamical systems
Hybrid automata extend traditional automata by embedding continuous-time dynamics within each discrete state. This framework supports formal verification, reachability analysis, and model-based design for safety-critical applications such as autonomous vehicles and aerospace systems.
Piecewise affine systems
Piecewise affine models approximate nonlinear dynamics by dividing the operational space into regions, each governed by an affine equation. This approach balances modeling fidelity with tractable analysis and control, making it popular in power electronics and robotics.
Stochastic or probabilistic hybrid systems
In stochastic hybrid systems, randomness is woven into both discrete transitions and continuous trajectories. This category is essential when accounting for noise, disturbances, and probabilistic events, and it supports reliability analysis and probabilistic verification.
Summary
Hybrid systems unite discrete decision-making with continuous dynamics. The four main categories—switched systems, hybrid automata, piecewise affine systems, and stochastic hybrid systems—provide a practical framework for modeling, analysis, and control across engineering disciplines. Understanding where a system fits helps researchers pick appropriate tools, ensure safety and performance, and guide effective design.
