By Panos J. Antsaklis

ISBN-10: 0817644601

ISBN-13: 9780817644604

In response to a streamlined presentation of the authors’ profitable paintings Linear structures, this textbook presents an advent to structures concept with an emphasis on keep watch over. preliminary chapters current priceless mathematical heritage fabric for a basic realizing of the dynamical habit of structures. every one bankruptcy contains valuable bankruptcy descriptions and guidance for the reader, in addition to summaries, notes, references, and workouts on the finish. The emphasis all through is on time-invariant platforms, either non-stop- and discrete-time.

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**Additional info for A Linear Systems Primer**

**Sample text**

Assume that ˙ θ(0) and θ(0) are given. 12. Assume that θ1 (0), θ2 (0), θ˙1 (0), and θ˙2 (0) are given. 2. 11. 12. Two link pendulum resistors in electric circuits, then we can use Lagrange’s equation to describe such systems. ) For a system with n degrees of freedom, this equation is given by ∂D ∂L d ∂L (q, q) ˙ + (q, q) ˙ − (q) ˙ = fi , i = 1, . . 97) dt ∂ q˙i ∂q ∂ q˙i where q T = (q1 , . . , qn ) denotes the generalized position vector. , the diﬀerence between the kinetic energy T and the potential energy W .

Qn ) denotes the generalized position vector. , the diﬀerence between the kinetic energy T and the potential energy W . , [βij ] is symmetric and all of its eigenvalues are nonnegative). The dissipation function D represents onehalf the rate at which energy is dissipated as heat. It is produced by friction in mechanical systems and by resistance in electric circuits. 97) denotes an applied force and includes all external forces associated with the qi coordinate. The force fi is deﬁned as being positive when it acts to increase the value of the coordinate qi .

Linearize this system about the point xT = (0, 0). By means of computer simulations, compare solutions corresponding to diﬀerent initial conditions in the vicinity of the origin of the above system of equations and its linearization. (b) Linearize the (bilinear control) system x ¨ + (3 + x˙ 2 )x˙ + (1 + x + x2 )u = 0 about the solution x = 0, x˙ = 0, and the input u(t) ≡ 0. As in part (a), compare (by means of computer simulations) solutions of the above equation with corresponding solutions of its linearization.

### A Linear Systems Primer by Panos J. Antsaklis

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