ISSN:
1531-5878
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract We consider the concept reachability for Polynomial Matrix Descriptions (PMDs); i.e., systems of the form ∑: A(ρ)β(t)=B(ρ)u(t),y(t)=C(ρ)β(t), whereρ:=d/dt the differential operator,A(ρ)=A0+A1 ρ+...+ Av ρ v εR r×r[ρ], AiεR r×r,i=0, 1,..., ν ≥ 1 with rank R A v ≤r B(ρ) =B 0+B 1ρ+...+B σρσ εR r×m[ρ], Bi εR r×m,i=0,1,...,σ ≥ 0 C(ρ)=C0+C1 ρ+...+Cσ1 ρ σ1 εR m1×r[ρ],C i εR m1×r ,i=0, 1,..., σ1 ≥ 0, β(t): (0−, ∞) →R r is the pseudostate of (∑),u(t): [0, ∞) →R m is the control input to (∑), and y(t) is the output of the system (∑). Starting from the fact that generalized state space systems, i.e., systems of the form ∑1: Ex(t)=Ax(t)+ Bu(t), y(t)=Cx(t), whereE εR r×r, rank R E 〈r, A εR r×r,B εR r×m,C εR m1×r represent a particular case of PMDs, we generalize various known results regarding the smooth and impulsive solutions of the homogeneous and the nonhomogeneous system (∑1) to the more general case of PMDs (∑). Relying on the above generalizations we develop a theory regarding the reachability of PMDs using time-domain analysis, which takes into account finite and infinite zeros of the matrix A(s)=L.[A(ρ)]. The present analysis extends in a general way many results previously known only for regular and generalized state space systems.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01204685
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