Robust Control of Linear Systems Subject to Uncertain by Francesco Amato

By Francesco Amato

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"This ebook presents a scientific therapy of the idea of strong keep watch over of dynamical platforms. … the writer has selected to contemplate in simple terms the issues for which a definitive resolution has been stumbled on, having in brain researchers or engineers operating in industries who are looking to practice those methodologies to sensible keep watch over difficulties. … The presentation is self contained, all proofs are given in addition to genuine global examples. … The self contained presentation makes it compatible for use for academic post-graduate purposes." (Anna Maria Perdon, Zentralblatt MATH, Vol. 1142, 2008)

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Additional resources for Robust Control of Linear Systems Subject to Uncertain Time-Varying Parameters

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1) for all admissible (in the sense specified below) time realizations of the parameters. 1. 1) is QS. 4) is exponentially stable. ˜ := A(p(·)) ∈ PC(R+ , Rn×n ); thereProof. Let p(·) ∈ PC(R+ , R). 1. 3) implies that there exists a positive definite matrix P such that A˜T P + P A˜ << 0 . 1 (applied with a constant P ) and the arbitrariness of the function p(·) ∈ PC(R+ , R). 1. 1 is the use of a constant quadratic Lyapunov function in the form v(x) = xT P x. e. a bound on the rate of variation) it is more convenient to use quadratic Lyapunov functions which depend on parameters.

2q , h where p(hi) is the i-th vertex of Sh . If for some pair (h, i) the test fails then stop, the system is not quadratically stable. Step 3 Split each element belonging to S into 2q hyper-boxes, put them in S and goto Step 2. ✸ 58 Chapter 3. 3 converges into a finite number of iterations. 3 terminates in a finite number of iterations or the sequence of the positive definite matrices, generated from the iterative solution of the necessary test at Step 2 of the algorithm, is unbounded. 3 Other Approaches for Quadratic Stability Analysis When there are many non-multi-affine functions in the expression of A(·) or q, the number of parameters, is big it may be difficult to apply the approaches of Sects.

This results from reasonable physical considerations. Indeed following the assigned path, the number of passengers in the bus does not change (so the mass is time-invariant); on the other hand, velocity may vary. Our objective in the following is to verify whether the system in Fig. 13 is robustly stable, that is whether it is exponentially stable wrt the constant parameter p1 (mass) and the time-varying parameter p2 (velocity). 7). Obviously, exponential stability versus the parameter p2 is guaranteed by quadratic stability.

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