Controllability Of Delay-differential Systems Research Articles

Relative controllability of delay differential systems with impulses and linear parts defined by permutable matrices

This paper investigates the relative controllability of delay differential systems with linear impulses and linear parts defined by permutable matrices. We use the impulsive delay Grammian matrix to discuss the relatively controllability of impulsive linear delay controlled systems and we use the Krasnoselskii's fixed point theorem to discuss the relatively controllability of impulsive semilinear delay controlled systems. Finally, two examples are presented to illustrate our theoretical results.

Boundary Controllability of Delay Differential Systems of Fractional Order with Nonlocal Condition

Sufficient conditions for boundary controllability of time varying delay differential systems of fractional order with nonlocal condition in Banach space are established. The results are obtained by using fixed point theorems. An example is provided to illustrate our results.

Further results on the pointwise controllability of delay-differential systems

By expressing the recursive matrices in the controllability matrix of the delay-differential systems in terms of the sums of the two system matrices and their powers, a different controllability matrix is obtained. When the first system matrix takes the companion form and the sum of the two system matrices also takes the companion form, the controllability condition is expressed in terms of relative primeness of polynomials by means of our first result and previous results in time-invariant systems.

On the controllability of delay-differential systems

The output controllability condition of the class of time-invariant multivariable linear delay-differential systems is investigated by using an algebraic approach. The controllability condition is given in terms of the kernel of a map, which determines the behaviour of output after time t = 0 due to input up to t = 0. This kernel is then completely characterized by a module generated by the columns of a matrix directly computable from the system transfer function. It is shown that every reachable output of the system considered can be controlled to zero in finite time. This paper is intended to form a part of the first stage in the development of an operator transfer function approach to the design of certain class of infinite dimensional systems which commonly occur in industry and other fields.

On degeneracy of functional-differential equations

Publisher Summary This chapter discusses degeneracy of functional differential equations. The conjecture that linear difference-differential equations with constant coefficients are point-wise complete was presented in an earlier paper on controllability of delay-differential systems. At that time, it was known that nonautonomous systems need not to be point-wise complete. If a certain matrix has full rank, then contrary to the situation in the case of ordinary differential equations, this is sufficient for ℝ n null-controllability of a linear delay system. To make this rank condition also necessary for ℝ n null-controllability, one has to assume point-wise completeness of the system.

Algebraic and transfer-function criteria of fixed-time controllability of delay-differential systems†

Sufficient algebraic and transfer-function criteria of fixed-time controllability of linear time-invariant delay-differential system of the form [xdot](t) = Ax(t) + Bx(t-h) + Cu(t),x(t)∊Rn u(t)eRm are given. It is shown that those criteria are also necessary if the system is pointwise complete. It is known that if (1) rank B=l, (2) rank B = n,(3) n = 2, the above system is always point-wise complete and in these cases the algebraic and transfer function criteria of fixed-time controllability are both necessary and sufficient.

On the Controllability of Delay-Differential Systems

Controllability type applicable to optimal control problems for systems described by delay differential equations