Journal ArticleDOI
General aggregation of large-scale systems by vector Lyapunov functions and vector norms
TLDR
In this paper, a new approach is proposed to an advantageous application of both vector Lyapunov functions and vector norms to aggregation of large-scale systems, which reduces the stability test to verification of either the Popov criterion or stability of constant matrices of order reduced to the number equal to, or possibly less than, the number of subsystems.Abstract:
A new approach is proposed to an advantageous application of both vector Lyapunov functions and vector norms to aggregation of large-scale systems. As a result, the test of the stability property of a large-scale system is achieved without knowledge of stability properties of its subsystems. Furthermore, new completely relaxed stability conditions are established for non-stationary non-linear dynamic large-scale systems, which reduce the stability test to verification of either the Popov criterion or stability of constant matrices of order reduced to the number equal to, or possibly less than, the number of the subsystems. As by-products of the paper, linear and Aiserman conjectures are proved for classes of systems on arbitrary hierarchical level.read more
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Feedback control of large-scale systems
TL;DR: A survey of the results and open problems in feedback control of large-scale systems of multivariable feedback systems and structure of interconnected systems.
Journal ArticleDOI
Second-order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum
TL;DR: In this article, a second order sliding mode control synthesis for underactuated mechanical systems, operating under uncertainty conditions, is presented. But it does not rely on the generation of first order sliding modes, while providing robustness features similar to those possessed by their standard sliding mode counterparts.
Journal ArticleDOI
Stability analysis of large-scale systems composed of strongly coupled similar subsystems
TL;DR: A sufficient condition is derived that can be successfully used for typical large-scale systems with a large number of subsystems and strong subsystem interactions and is demonstrated by proving the stability of a large multiarea power system, for which stability tests that are based on weak subsystem interactions fail.
Proceedings ArticleDOI
Fuzzy control of a mobile robot: a new approach
TL;DR: A general analysis and design method are proposed to stabilize the dynamics of the mobile robot interpolated by two linear systems with two fuzzy rules based on converting the Stability analysis of a fuzzy control system to the stability analysis of an overvaluing system for the mobile Robot.
Journal ArticleDOI
On practical stability with the settling time via vector norms
Wilfrid Perruquetti,Wilfrid Perruquetti,Jean-Pierre Richard,Jean-Pierre Richard,Lj. Grujić,Pierre Borne +5 more
TL;DR: In this article, the authors give a workable method for practical stability study of nonlinear time-varying disturbed systems with settling time, using vector norms, which allow estimation of initial, final, admissible subsets of state space related to chosen settling time and final time.
References
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Journal ArticleDOI
Mathematical Methods of Optimal Control
Journal ArticleDOI
Asymptotic stability and instability of large-scale systems
TL;DR: In this paper, the authors extended the application of Lyapunov's theory to stability analysis of large-scale dynamic systems by redefining interconnection functions among the subsystems according to interconnection matrices, which can be used to determine connective asymptotic stability of large scale systems under arbitrary structural perturbations.
Journal ArticleDOI
A generalization of the Popov criterion
TL;DR: A criterion for the stability of control systems which contain an arbitrary finite number of memoryless nonlinearities reduces to the original Popov criterion when the absolute stability of a control system having one memorylessNonlinearity is considered.
Journal ArticleDOI
Stability regions of large-scale systems
TL;DR: In this article, three different forms of Liapunov functions are used for describing the stability behavior of the aggregated system, but one form in particular, heretofore not used in this context, is found to be the most natural.