Sensor Failure–Tolerant Observer Design With Regional Pole Placement

The purpose of this letter is to design a failure-tolerant observer that meets pole position constraints to enhance the observer’s response under various sensor failure scenarios while optimizing the nominal performance, measured by a disturbance rejection metric. A failure-tolerant observer design methodology based on the regional pole placement (RPP) technique is provided. The number of sensors
${m}$
and a minimum number of assumed functional sensors
${p}$
define the range of failure situations. Thus,
${p}$
specifies a failure tolerance level for the observer design. A semi-definite relaxation (SDR) technique is presented to alleviate the computational burden imposed by a large number of evaluated failure situations. The SDR method results in only a few linear matrix inequality sufficient conditions to solve the problem, but at the expense of reduced optimal performance. To compensate, the Hadamard and block Hadamard product approaches are suggested to provide more degrees of freedom in searching for the optimal solution. To demonstrate the efficacy of the failure-tolerant observer design, two illustrative examples are provided.