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On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients

Ludovic Rifford (2001)

ESAIM: Control, Optimisation and Calculus of Variations

Let x ˙ = f ( x , u ) be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke’s generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...

On the existence of nonsmooth control-Lyapunov functions in the sense of generalized gradients

Ludovic Rifford (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Let x ˙ = f ( x , u ) be a general control system; the existence of a smooth control-Lyapunov function does not imply the existence of a continuous stabilizing feedback. However, we show that it allows us to design a stabilizing feedback in the Krasovskii (or Filippov) sense. Moreover, we recall a definition of a control-Lyapunov function in the case of a nonsmooth function; it is based on Clarke's generalized gradient. Finally, with an inedite proof we prove that the existence of this type of control-Lyapunov...

Pole placement and mixed sensitivity of LTI MIMO systems having controlled outputs different from measurements

Miguel A. Flores, René Galindo (2021)

Kybernetika

Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) controllable and observable systems where the controller has access to some plant outputs but not others are considered. Analytical expressions of coprime factorizations of a given plant, a solution of the Diophantine equation and the two free parameters of a two-degrees of freedom (2DOF) controller based on observer stabilizing control are presented solving a pole placement problem, a mixed sensitivity criterion, and a reference tracking...

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.

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