Output Feedback Stabilization of Linear Systems

Cover Output Feedback Stabilization of Linear Systems
Output Feedback Stabilization of Linear Systems
Chen, Raymond
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(V) x(t) = ax(t) + bx(t-l) + u, y = cx(t) + dx(t-l), u = ky where a, b, c, d, k are real numbers.
Our purpose is to determine the existence of a real number k such that the corresponding characteristic equation of (P) A + (a + kc) + (b + kd)e~ A = (4.1) has only roots in the left half complex plane. Note that ~ ~ ~ ^2~2 with a, b, c, d fixed and c + d * 0, the set of all the coefficients of (4.1) which arise from all possible choices of k e R forms a straight line H = {(a,b)|ad - be - (ad + be)
... = 0) (4.2) Now, consider an exponential polynomial equation of the form A + a + be~ A =0 (4.3) 48 Let V a denote the set {(a,b) e R | \ t- a f be~* = implies ReX . In particular, when a = we call the domain of stability of (4.3). Thus, a system (V) is stabilizable if and only if H n P Q x $ . As in the previous chapters, we will study two main problems related to V : (i) the convex a hull of P q and (ii) the characterization of hyperplanes (straiqht lines) which intersect V .

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