Periodic observer design for networked embedded control systems

In this paper periodic observer design for linear continuous-time systems with periodically time-varying sampling intervals and time delays is considered. Such systems arise e.g. in networked embedded control applications where limited computation and communication resources have to be scheduled. A periodically time-varying discrete-time plant model and cost function regarding the timing effects are derived for the observer design. The design problem is formulated as a periodic linear quadratic (LQ) optimization problem. By applying the lifting procedure, this periodically time-varying LQ problem is transformed into a standard time-invariant LQ problem. The observer gain then follows from solving a periodic algebraic Riccati equation. Both a prediction and a current state observer are derived. Moreover, the separation principle for periodic systems is proved and observability is analyzed. The periodic observer design is illustrated for a benchmark system.