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A hierarchical decomposition of decision process Petri nets for modeling complex systems

Julio Clempner (2010)

International Journal of Applied Mathematics and Computer Science

We provide a framework for hierarchical specification called Hierarchical Decision Process Petri Nets (HDPPNs). It is an extension of Decision Process Petri Nets (DPPNs) including a hierarchical decomposition process that generates less complex nets with equivalent behavior. As a result, the complexity of the analysis for a sophisticated system is drastically reduced. In the HDPPN, we represent the mark-dynamic and trajectory-dynamic properties of a DPPN. Within the framework of the mark-dynamic...

A Lyapunov functional for a system with a time-varying delay

Józef Duda (2012)

International Journal of Applied Mathematics and Computer Science

The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

A Lyapunov-based design tool of impedance controllers for robot manipulators

Marco Mendoza, Isela Bonilla, Fernando Reyes, Emilio González-Galván (2012)

Kybernetika

This paper presents a design tool of impedance controllers for robot manipulators, based on the formulation of Lyapunov functions. The proposed control approach addresses two challenges: the regulation of the interaction forces, ensured by the impedance error converging to zero, while preserving a suitable path tracking despite constraints imposed by the environment. The asymptotic stability of an equilibrium point of the system, composed by full nonlinear robot dynamics and the impedance control,...

A model-based fault detection and diagnosis scheme for distributed parameter systems : a learning systems approach

Michael A. Demetriou (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this note, fault detection techniques based on finite dimensional results are extended and applied to a class of infinite dimensional dynamical systems. This special class of systems assumes linear plant dynamics having an abrupt additive perturbation as the fault. This fault is assumed to be linear in the (unknown) constant (and possibly functional) parameters. An observer-based model estimate is proposed which serves to monitor the system’s dynamics for unanticipated failures, and its well...

A Model-Based Fault Detection and Diagnosis Scheme for Distributed Parameter Systems: A Learning Systems Approach

Michael A. Demetriou (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this note, fault detection techniques based on finite dimensional results are extended and applied to a class of infinite dimensional dynamical systems. This special class of systems assumes linear plant dynamics having an abrupt additive perturbation as the fault. This fault is assumed to be linear in the (unknown) constant (and possibly functional) parameters. An observer-based model estimate is proposed which serves to monitor the system's dynamics for unanticipated failures, and its well...

A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems

Danica Rosinová, Vojtech Veselý, Vladimír Kučera (2003)

Kybernetika

Necessary and sufficient conditions for a discrete-time system to be stabilizable via static output feedback are established. The conditions include a Riccati equation. An iterative as well as non-iterative LMI based algorithm with guaranteed cost for the computation of output stabilizing feedback gains is proposed and introduces the novel LMI approach to compute the stabilizing output feedback gain matrix. The results provide the discrete- time counterpart to the results by Kučera and De Souza.

A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models

Ibtissem Abdelmalek, Noureddine Goléa, Mohamed Hadjili (2007)

International Journal of Applied Mathematics and Computer Science

In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization....

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

Saleh Mobayen, Fairouz Tchier (2015)

Kybernetika

This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained...

A new method to obtain decay rate estimates for dissipative systems with localized damping.

Patrick Martínez (1999)

Revista Matemática Complutense

We consider the wave equation damped with a locally distributed nonlinear dissipation. We improve several earlier results of E. Zuazua and of M. Nakao in two directions: first, using the piecewise multiplier method introduced by K. Liu, we weaken the usual geometrical conditions on the localization of the damping. Then thanks to some new nonlinear integral inequalities, we eliminate the usual assumption on the polynomial growth of the feedback in zero and we show that the energy of the system decays...

A new method to obtain decay rate estimates for dissipative systems

Patrick Martinez (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the wave equation damped with a boundary nonlinear velocity feedback p(u'). Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimate even if the function ρ has not a polynomial behavior in zero. This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction...

A new Nyquist-based technique for tuning robust decentralized controllers

Alena Kozáková, Vojtech Veselý, Jakub Osuský (2009)

Kybernetika

An original Nyquist-based frequency domain robust decentralized controller (DC) design technique for robust stability and guaranteed nominal performance is proposed, applicable for continuous-time uncertain systems described by a set of transfer function matrices. To provide nominal performance, interactions are included in individual design using one selected characteristic locus of the interaction matrix, used to reshape frequency responses of decoupled subsystems; such modified subsystems are...

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