Interval Observers for Hybrid Continuous-Time Stationary Systems

The problem of designing interval observers for hybrid continuous stationary systems under external disturbances and measurement noise is studied. It is assumed that the continuous dynamics of such a system is described by a linear or nonlinear differential equation of state with a linear output function. The values of the system’s parameters depend on the region reached by its state and are switched using a control system (CS) with a finite number of states. The relations that allow designing a hybrid interval observer of the minimal dimension that is guaranteed to estimate the set of admissible values of the prescribed linear vector function of the system’s states are derived. To solve the problem, pair algebra of partitions and linear algebra are used. The theoretical results are illustrated by an example.