Stabilization of systems with variable and uncertain sampling period and time delay

Stability and control issues of systems with uncertain and time-varying sampling period and time-delay are addressed in this paper. These arise, e.g., in embedded or networked control applications where limited computation or communication resources have to be scheduled. The uncertain and time-varying sampling period and time delay are transformed into polytopic and additive norm-bounded uncertainties in the discretized system description. Control design and stability analysis methods are given in the form of LMIs applying switched parameter-dependent quadratic Lyapunov functions. Two reduction algorithms are proposed in order to decrease the amount of LMIs necessary for stability analysis. The control design and stability analysis methods as well as the reduction algorithms are illustrated by an example.