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Rank-one LMI approach to robust stability of polynomial matrices

Didier Henrion, Kenji Sugimoto, Michael Šebek (2002)

Kybernetika

Necessary and sufficient conditions are formulated for checking robust stability of an uncertain polynomial matrix. Various stability regions and uncertainty models are handled in a unified way. The conditions, stemming from a general optimization methodology similar to the one used in μ -analysis, are expressed as a rank-one LMI, a non-convex problem frequently arising in robust control. Convex relaxations of the problem yield tractable sufficient LMI conditions for robust stability of uncertain...

Robust controller design for linear polytopic systems

Vojtech Veselý (2006)

Kybernetika

The paper addresses the problem of the robust output feedback controller design with a guaranteed cost and parameter dependent Lyapunov function for linear continuous time polytopic systems. Two design methods based on improved robust stability conditions are proposed. Numerical examples are given to illustrate the effectiveness of the proposed methods. The obtained results are compared with other three design procedures.

Robust decoupling through algebraic output feedback in manipulation systems

Paolo Mercorelli (2010)

Kybernetika

This paper investigates the geometric and structural characteristics involved in the control of general mechanisms and manipulation systems. These systems consist of multiple cooperating linkages that interact with a reference member of the mechanism (the “object”) by means of contacts on any available part of their links. Grasp and manipulation of an object by the human hand is taken as a paradigmatic example for this class of manipulators. Special attention is devoted to the output specification...

Robust exponential stability of a class of nonlinear systems

Vojtech Veselý, Danica Rosinová (1998)

Kybernetika

The paper addresses the problem of design of a robust controller for a class of nonlinear uncertain systems to guarantee the prescribed decay rate of exponential stability. The bounded deterministic uncertainties are considered both in a studied system and its input part. The proposed approach does not employ matching conditions.

Robust hierarchical sliding mode control with state-dependent switching gain for stabilization of rotary inverted pendulum

Muhammad Idrees, Shah Muhammad, Saif Ullah (2019)

Kybernetika

The rotary inverted pendulum (RIP) system is one of the fundamental, nonlinear, unstable and interesting benchmark systems in the field of control theory. In this paper, two nonlinear control strategies, namely hierarchical sliding mode control (HSMC) and decoupled sliding mode control (DSMC), are discussed to address the stabilization problem of the RIP system. We introduced HSMC with state-dependent switching gain for stabilization of the RIP system. Numerical simulations are performed to analyze...

Robust observer-based finite-time H ∞ control designs for discrete nonlinear systems with time-varying delay

Yali Dong, Huimin Wang, Mengxiao Deng (2021)

Kybernetika

This paper investigates the problem of observer-based finite-time H ∞ control for the uncertain discrete-time systems with nonlinear perturbations and time-varying delay. The Luenberger observer is designed to measure the system state. The observer-based controller is constructed. By constructing an appropriated Lyapunov-.Krasovskii functional, sufficient conditions are derived to ensure the resulting closed-loop system is H ∞ finite-time bounded via observer-based control. The observer-based controller...

Robust pole placement for second-order systems: an LMI approach

Didier Henrion, Michael Šebek, Vladimír Kučera (2005)

Kybernetika

Based on recently developed sufficient conditions for stability of polynomial matrices, an LMI technique is described to perform robust pole placement by proportional-derivative feedback on second-order linear systems affected by polytopic or norm-bounded uncertainty. As illustrated by several numerical examples, at the core of the approach is the choice of a nominal, or central quadratic polynomial matrix.

Robust stability of non linear time varying systems

Ezra Zeheb (1999)

Kybernetika

Systems with time-varying non-linearity confined to a given sector (Luré type) and a linear part with uncertainty formulated by an interval transfer function, are considered. Sufficient conditions satisfying the Popov criterion for stability, which are computationally tractable, are derived. The problem of checking the Popov criterion for an infinite set of systems, is reduced to that of checking the Popov criterion for a finite number of fixed coefficient systems, each in a prescribed frequency...

Robust stability of positive continuous-time linear systems with delays

Mikołaj Busłowicz (2010)

International Journal of Applied Mathematics and Computer Science

The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.

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