Global Robust Stability Research Articles

Stabilization of Nonlinear Systems with Norm Bounded Uncertainties

In this paper, we give a necessary and sufficient condition in terms of Hamilton-Jacobi inequalities for globally stabilizing a nonlinear system, robustly with respect to unstructured uncertainties, depending both on unknown time-varying parameters Δ(t) and state x and norm-bounded for each x. This condition essentially states that global robust stabilization via smooth (except possibly at the origin) controllers is equivalent to the existence of a robust control Lyapunov function, which requires the solution of a suitable Hamilton Jacobi inequality, and generalizes a well-known condition for linear systems. This clarifies also the connection between robust stabilization and H∞ control for nonlinear systems.

Global robust stabilization of nonlinear cascaded systems

This paper gives a sufficient condition for a class of nonlinear cascaded systems to be globally stabilizable via state feedback in the presence of uncertainty which does not necessarily satisfy the so-called matching condition. The authors' result is an extension of the former stabilization results which treated systems without uncertainty, in the sense that the uncertainty is taken into account. >

The robust global stabilization of a stirred tank reactor

In this paper, a program of analysis is carried out for control of a nonlinear stirred tank reactor. By examining the uniqueness and stability properties of the reactor, the zero dynamics are analyzed. Subsequently, a model reference adaptive controller (MRAC) which explicitly takes into account the nonlinearities of the system is designed; the MRAC successfully compensates for parametric uncertainty. It is shown that even when almost all reactor parameters are unknown, global convergence over the entire phase space is achieved.

マッチング条件を満たさない不確実要素を含む非線形システムの大域的ロバスト安定化

マッチング条件を満たさない不確実要素を含む非線形システムの大域的ロバスト安定化

Robust stability of multi‐loop continuous time self‐tuning controllers

AbstractThe results of an earlier paper concerning global robustness of single‐loop self‐tuning controllers are extended to include multiple self‐tuning controllers operating in a multiple‐interacting‐loop environment. The robust stability is shown to depend on the singular value loci of a certain transfer function matrix. The need for control weighting to ensure global robust stability is emphasized.

On global stability of adaptive systems using an estimator with parameter freezing

The results of R. Kosut and B. Friedlander (1985) on robust global stability of direct adaptive controllers using an integral adaptation law are extended to the case where the adaptation algorithm includes a parameter freezing mechanism, i.e. the control parameters are held constant at certain time intervals. The authors' main concern is to propose an estimator with freezing capabilities which preserve the property needed for the global stability analysis, namely, that it defines a passive operator. In an adaptive control context, the additional degree of freedom provided by the freezing imposes no further assumptions for global stability. A crucial requirement for the analysis is that the number of freezing intervals is finite.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust adaptive algorithm with non-linear decay term

A new modified adaptive algorithm with a non-linear decay term is proposed to guarantee the robust global stability of continuous-time model reference adaptive control (MRAC) systems to unmodelled dynamics in the plant. The fundamental approach is due to Kosut and Friedlander (1985), but different robust stability results and adaptive features are shown because of the non-linear decay term. A sufficient condition to find the design parameters in the decay term which ensure the robust result is proved and its dependence on the tuned gains and unmodelled dynamics is discussed. The merits and demerits of our new algorithm are also discussed using a simple example for illustration.