Discretization and discrete-time output feedback control of linear parameter varying continuous-time systems

This paper is concerned with the problem of discretization and discrete-time output feedback control design for polytopic continuous-time linear parameter-varying (LPV) systems with network-induced delay. Using a constant sampling period and an extension of the Taylor series expansion applied to the exponential of a parameter-dependent matrix, a discretized model whose matrices depend polynomially on the time-varying parameters that are used to schedule the control gain is obtained. The discrete-time model also has additive norm bounded terms, representing the discretization errors, and a network-induced delay in the control signal. A two-step strategy based on linear matrix inequality (LMI) conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the original continuous-time LPV system. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through a numerical example.