Causal Gain-scheduled output feedback controllers using parameter-dependent Lyapunov Functions

Abstract

This paper addresses the design problem of Gain-Scheduled Output Feedback (GSOF) controllers, in which causality with respect to (w.r.t) scheduling parameters in the GSOF controllers is kept, for continuous-/discrete-time Linear Parameter-Varying (LPV) systems using Parameter-Dependent Lyapunov Functions (PDLFs). In general, continuous-time GSOF controllers designed by conventional methods, i.e. so-called change-of-variables using PDLFs, depend on the derivatives of scheduling parameters, and discrete-time GSOF controllers designed by conventional methods or extended Linear Matrix Inequality (LMI) technique using parameter-dependent auxiliary matrices both depend on the one-step-ahead scheduling parameters. These mean that the designed GSOF controllers are not implementable to practical systems due to the non-causality w.r.t. scheduling parameters. On this issue, we propose a formulation which circumvents the causality problem by replacing the term that introduces the causality issue with another term via the reverse use of the Elimination lemma which is also known as “S-variable” approach. A toy example and a practical example (lateral-directional motion control around wing level flight of JAXA’s research airplane MuPAL-α) are included to demonstrate the effectiveness compared to the existing methods.