Fixed-time incremental passivity for switched nonlinear systems and its application to output regulation

Passivity is often useful for systems with an origin equilibrium. However, many practical systems have multiple equilibria or no equilibrium. This paper explores fixed-time incremental passivity for switched nonlinear systems using multiple incremental storage functions and applies this concept to address the fixed-time full-information output regulation problem. First, fixed-time incremental passivity is defined, allowing storage functions to increase at each switching time, ensuring that each active subsystem demonstrates fixed-time incremental passivity. Second, a more general switching law based on state information is provided to achieve fixed-time incremental passivity. This switching law employs continuous functions instead of storage functions, thereby offering greater design flexibility. Third, the developed fixed-time incremental passivity theory is utilized for fixed-time output regulation, even when individual subsystems lack fixed-time incremental passivity. Finally, the effectiveness of this control approach is illustrated through two examples.