H_∞ controller design for a class of nonideal switched systems

A class of smoothly switched system model was proposed to describe the phenomena of dynamics switching that generally occured in real-world processes, and the problem of robust H_∞ switching controller design was investigated for systems of this kind. Based on the average dwell time method and the differential inequality theory, the sufficient condition was presented such that asymptotic stability and some given L₂ gain are guaranteed for the smoothly switched system. The design criterion of the robust H_∞ switching controller was further obtained in terms of linear matrix inequalities. The smoothly switched system model covers the prevailing switched system model as a special case; therefore the controller synthesis method in this note is applicable to traditional switched systems. A design example on a morphing aircraft illustrates that the resultant tracking control system qualifies well robustness against parameter uncertainties while possessing stability and acceptable tracking performance.