Observer Design For Discrete Retangular Singular Systems With Time-Delay

The paper considers the problem of observer design for discrete rectangular singular systems with time-delay. First, the observer design for discrete rectangular singular systems with constant time-delay is discussed. The system is described by the following form:where x(k)∈Rⁿ is the state vector, u(k)∈R^p is the controlled input,y(k)∈R^q is the measurable output, z(k)∈R^l is the estimated output;E,A,A_d∈R^m×n,B∈R^m×p,C,C_d∈R^q×n,D∈R^q×p,L∈R^l×nare constant matrices, Eis a singular matrix, rankE =r0, d>0 is a known integer delay.To design an observer for system (2-1) as follows:such that for any admissible initial value it satisfies that At first, it is assumed that rankE = r