Introduction to Mathematical Systems Theory: Linear Systems, by Christiaan Heij, André C.M. Ran, F. van Schagen

By Christiaan Heij, André C.M. Ran, F. van Schagen

This ebook presents an advent to the idea of linear platforms and keep an eye on for college students in company arithmetic, econometrics, laptop technological know-how, and engineering. the point of interest is on discrete time structures, that are the main suitable in enterprise purposes, instead of non-stop time structures, requiring much less mathematical preliminaries. the themes taken care of are one of the imperative themes of deterministic linear method conception: controllability, observability, recognition conception, balance and stabilization via suggestions, LQ-optimal keep watch over conception. Kalman filtering and LQC-control of stochastic platforms also are mentioned, as are modeling, time sequence research and version specification, in addition to version validation. routines utilizing MATLAB, awarded on an accompanying CD, increase the most strategies and methods within the text.

Show description

Read or Download Introduction to Mathematical Systems Theory: Linear Systems, Identification and Control PDF

Best control systems books

Modeling and Control of Complex Physical Systems: The Port-Hamiltonian Approach

Strength alternate is an important starting place of the dynamics of actual structures, and, as a result, within the learn of complicated multi-domain structures, methodologies that explicitly describe the topology of strength exchanges are instrumental in structuring the modeling and the computation of the system's dynamics and its keep watch over.

Intelligent Diagnosis and Prognosis of Industrial Networked Systems (Automation and Control Engineering)

In an period of in depth pageant the place plant working efficiencies has to be maximized, downtime as a result of equipment failure has turn into extra high priced. to chop working expenditures and raise sales, industries have an pressing have to expect fault development and final lifespan of commercial machines, tactics, and platforms.

Fault Detection and Diagnosis in Engineering Systems

That includes a model-based method of fault detection and prognosis in engineering platforms, this e-book comprises up to date, sensible info on fighting product deterioration, functionality degradation and significant equipment harm. ;College or college bookstores may possibly order 5 or extra copies at a unique scholar fee.

Additional info for Introduction to Mathematical Systems Theory: Linear Systems, Identification and Control

Sample text

This implies that a > 0 and b < 0. From the above result for general second order difference equations it follows that this system is asymptotically stable if and only if b > −1 and a + b < 1, that is, βδ < 1 and β < 1. The last restriction is plausible for economic reasons, while the first restriction means that investors should not react too strongly to increased consumption. Finally, the path towards equilibrium will show oscillations if the characteristic roots of the 4δ equation are non-real, that is, if a2 + 4b < 0, or equivalently, β < (1+δ) 2.

Let Θ = (A, B, C, D) be a realization with state space dimension n. Then the following statements are equivalent. (i) Θ is controllable; (ii) rank A − λI B = n for each λ ∈ C; (iii) rank A − λI B = n for each eigenvalue λ of A; (iv) all eigenvalues of A are (A, B) controllable. 3 Structure Theory of Realizations In this section we describe the structure of state space representations of a given system. We pay particular attention to minimal realizations, that is, realizations with the lowest state space dimension.

Thus R(Θ) = Im B N (Θ) = AB . . An−1 B , n−1 Ker CAk . 8) 32 Chapter 3. ) ˙ 4 = Rn . (Here and in the sequel + R(Θ)}+X Let Xi have dimension ni , i = 1, 2, 3, 4, so that n1 + n2 + n3 + n4 = n, and let b1 , . . , bn be a basis for Rn ordered in such a way that the first n1 vectors are a basis for X1 , the next n2 vectors are a basis for X2 , the next n3 vectors from a basis of X3 , and finally, the last n4 vectors are a basis for X4 . Let S = b1 . . bn , so that S is invertible, and let Θ := (S −1 AS, S −1 B, CS, D).

Download PDF sample

Rated 4.78 of 5 – based on 11 votes