A dilated LMI approach to continuous-time gain-scheduled controller synthesis with parameter-dependent Lyapunov variables

This paper is concerned with the gain-scheduled controller synthesis for linear parameter varying (LPV) systems. In the case where the state space matrices of the system depend afrinely on the time-varying parameters, the standard linear matrix inequalities (LMI's) are helpful in dealing with such problems provided that we accept the notion of quadratic stability. However, in the case of rational parameter dependence, the standard LMI's carry some deficiency and do not lead to numerically tractable conditions in a straightforward fashion. This paper clarifies that recently developed dilated LMI's are effective in overcoming the difficulties and deriving numerically tractable conditions The dilated LMI's enable us also to employ parameterdependent Lyapunov variables to achieve control objectives, which are known to be promising to alleviate the conservatism stemming from a quadratic (parameter-independent) Lyapunov variable.