Abstract
In this paper the problem of practical stabilization for a significant class of MIMO uncertain pseudo-linear and pseudo-quadratic systems, with additional bounded nonlinearities and/or bounded disturbances, is considered. By using the concept of majorant system, via Lyapunov approach, new fundamental theorems, from which derive explicit formulas to design state feedback control laws, with a possible imperfect compensation of nonlinearities and disturbances, are stated. These results guarantee a specified convergence velocity of the linearized system of the majorant system and a desired steady-state output for generic uncertainties and/or generic bounded nonlinearities and/or bounded disturbances.
Highlights
For the above significant systems, it is important to design a control law such that, in a finite time interval, the state evolution, for all the initial conditions belonging to a specified compact set, is bounded and such that the evolution of the output converges, with assigned minimum velocity, to chosen maximum values, that are bounded and not necessarily null
In this paper a systematic method, in a more general framework with respect to the ones proposed in literature, for the analysis and for the practical stabilization of a significant class of MIMO uncertain pseudo-linear and pseudo-quadratic systems, with additional bounded nonlinearity and/or bounded disturbances, is considered
It is easy to prove that the point of contact of the hyper-line orthogonal to the versor ei,i 1, 2, n, of Rn and tangent to the hyper-ellipse E is pi i-th column of
Summary
The problem of practical stability and stabilization for linear and nonlinear systems subject to disturbances and parametric uncertainties together with an efficient robust control has been in the past [1-10] one of the most research topic and nowadays remains actual and significant [11-21]. [1-5,8-10,13-18]), for the analysis and for the practical stabilization of a significant class of MIMO uncertain pseudo-linear and pseudo-quadratic systems, with additional bounded nonlinearity and/or bounded disturbances, is considered. By using the concept of majorant system, via Lyapunov approach, new fundamental theorems, from which derive explicit formulas and efficient algorithms to design state feedback control laws, with a possible imperfect compensation of nonlinearities and disturbances, are stated. These results guarantee a specified convergence velocity of the linearized system of the majorant system and a desired steady-state output for generic uncertainties and/or generic bounded nonlinearities and/or bounded disturbances (see [19-21]). Two significant examples of application, well showing the utility and the efficiency of the proposed results, are reported
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