Piecewise functions are common in the mathematical modelling of various systems, including mechanical and electronic devices, demography and economy, and robotics and control equipment. Many studies of piecewise systems are addressed towards the analysis of their solutions using well-structured traditional and non-conventional techniques. In particular, stable and structurally stable solutions (robust stability), limit cycles, and strange attractors have been found in a wide variety of systems, including population dynamics, predator-prey models, disease models, human organs and health models, circuit design, mechanical systems, control and automation, neural networks, and Petri net design. Among other dynamical behaviours, chaos has also been extensively studied in piecewise systems in recent years.

Bifurcation theory is often applied in the study of oscillatory solutions. In addition, new methods for studying bifurcations in piecewise systems, for example, in Liénard and fuzzy systems, have been developed, including the use of mathematical models with uncertainties. In particular, in Mamdani fuzzy systems, logic design is equivalent to a saturated control system. In this sense, the fuzzy system theory can be used to generate a periodic motion (limit cycle) and strange attractors.

The main goal of this Special Issue is to publish results devoted to the development of theoretical models and application of piecewise dynamical systems in different fields of science and engineering. Authors are encouraged to submit original research or review articles on traditional and new research directions in the field of complex piecewise dynamical systems.

Potential topics include but are not limited to the following:

• Piecewise nonlinear systems
• Piecewise control systems
• Stability and robust stability of piecewise systems
• Chaos in piecewise systems
• Bifurcations in piecewise systems
• Piecewise linear unstable and dissipative systems
• Sectorial control systems
• Mathematical fuzzy modelling and control
• Saturation and relay controllers
• Sliding mode control for piecewise systems
• Liénard systems
• Limit cycle generation in piecewise systems
• Modelling and control of electromechanical systems
• Modelling and control of biological systems
• Piecewise systems in industrial processes and manufacturing problems
• Application of piecewise systems in automotive engineering and avionics
• Piecewise communication and transportation network systems
• Piecewise robotic systems