Stability and Stabilization of Linear Systems with by Sophie Tarbouriech

By Sophie Tarbouriech

It is famous that actuator saturation is found in virtually all keep an eye on platforms, the sign amplitude that an actuator can carry frequently being constrained by way of actual or safeguard constraints. forget of those amplitude bounds and the resultant actuator saturation could be a resource of functionality degradation or maybe instability of the closed-loop approach so an in-depth knowing of the phenomena as a result of saturation is of value in fixing and warding off difficulties in commercial keep an eye on structures.

Stability and Stabilization of Linear platforms with Saturating Actuators details either simple ideas and instruments basic for the research and synthesis of linear platforms topic to actuator saturation and, in a proper even though didactic style, advancements in fresh study. The authors think of a state-space technique and concentrate on the issues of balance research and the synthesis of stabilizing keep watch over legislation in either neighborhood and international contexts. varied tools of modeling the saturation and behaviour of the nonlinear closed-loop procedure are given specific consciousness. different types of Lyapunov services, polyhedral, quadratic and Lure-type, for instance, are thought of with the intention to current assorted inner in addition to exterior balance and stabilization stipulations. effects bobbing up from doubtful platforms and treating functionality within the presence of saturation also are given. linked to the various theoretical effects, the textual content proposes equipment and algorithms for computing estimates of the basin of allure and units of admissible exogenous signs in addition to for designing keep an eye on structures considering, a priori, the regulate bounds and the potential of saturation. moreover, the so-called anti-windup technique, which is composed of including an additional layer within the pre-designed keep watch over approach particularly to take on the bad results of saturation, is presented.

These tools and algorithms are according to using linear programming and linear matrix inequalities and will be simply carried out with MATLAB® and Scilab.

Stability and Stabilization of Linear platforms with Saturating Actuators is a beneficial reference for electric, mechanical, chemical and aeronautical engineers engaged on keep an eye on functions, in addition to graduate scholars and researchers drawn to the improvement of recent instruments and theoretical effects relating platforms with saturation.

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Moreover, it is also important to notice that a necessary condition to the asymptotic stability is that all the eigenvalues of (A + BK) are in the open left-half complex plane, since the system is linear in a neighborhood of the origin. For the control design problem, to take into account the control saturation occurrence allows, in general, to stabilize larger domains of admissible initial states without an important degradation of the required closed-loop performances. These aspects will be studied and illustrated in the next chapters of the book.

18) is the whole state space n . Solvability conditions for the global asymptotic stabilization problem for a linear system subject to saturating controls have been stated in the seminal works of Sontag and his co-authors: see, for example [329, 338, 403] in the case of continuous-time systems and [402] for the discrete-time systems. These works provide the following formal result. 2 is globally stabilizable if and only if 1. the pair (A, B) is stabilizable; 2. the eigenvalues of matrix A do not have positive real parts.

These admissible sets are in general characterized with respect to bounds on the amplitude (L∞ -norm) and/or the energy (L2 -norm) of w(t). This problem is also referred to as input-to-state stability analysis [215]. e w(t) = 0 for some t > t1 or limt→∞ w(t) = 0, the convergence of the trajectories to the equilibrium point x = 0 must be guaranteed. 15). Hence, considering a set W of admissible exogenous signals and a set X0 of admissible initial conditions we are generically interested in the following problem.

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