Quasi-LPV Systems
A quasi-LPV system refers to case where the parameter trajectory is a function of the system state and inputs, i.e. where
is the system state,
is the system input, and
is time. The term "quasi" is used to indicate that the parameter dependence actually introduces a nonlinearity in the system dynamics.
The current implementation of LPVtools treats quasi-LPV systems just like any other LPV system for the purposes of analysis and synthesis, i.e. the parameter is assumed to vary independently of the system's state and input. This assumption will result in conservative results when working with quasi-LPV systems in LPVTools. However, quasi-LPV systems can be simulated correctly using the lpvlsim, lpvstep, lpvimpulse, and lpvinitial functions in LPVTools. Specifically, the the parameter trajectory that is used in the simulation can be specified as a function of the state, input, and time.