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Robustness Analysis of Polynomials with Polynomial Parameter Dependency Using Bernstein Expansion
 IEEE TRANS. AUTOMAT. CONTR
, 1998
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Application of Bernstein Expansion to the Solution of Control Problems
 University of Girona
, 1999
"... We survey some recent applications of Bernstein expansion to robust stability, viz. checking robust Hurwitz and Schur stability of polynomials with polynomial parameter dependency by testing determinantal criteria and by inspection of the value set. Then we show how Bernstein expansion can be used t ..."
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Cited by 8 (0 self)
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We survey some recent applications of Bernstein expansion to robust stability, viz. checking robust Hurwitz and Schur stability of polynomials with polynomial parameter dependency by testing determinantal criteria and by inspection of the value set. Then we show how Bernstein expansion can be used to solve systems of strict polynomial inequalities.
Robust Stability Analysis of Bilateral Teleoperation Architectures for Admittance Type Devices
"... Abstract — One of the main challenges in telerobotics is the selection of control architectures and control parameters, which are able to robustly stabilize the overall teleoperation system despite of changing human operator and environment impedances. In this paper robust stability of different typ ..."
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Cited by 5 (4 self)
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Abstract — One of the main challenges in telerobotics is the selection of control architectures and control parameters, which are able to robustly stabilize the overall teleoperation system despite of changing human operator and environment impedances. In this paper robust stability of different types of bilateral control algorithms for admittance type devices is analyzed. Hereby stability of the system is investigated by using the parameter space approach, which allows the analysis of uncertain systems with varying plant parameters. Simple linear models are assumed for human operator, humansysteminterface, teleoperator as well as remote environment. The parameter space method is used for controller design as well as for robustness analysis. Finally Γstability of the presented architectures is evaluated for a one degree of freedom mechatronic teleoperation system. I.
Design And Analysis Of Robust Control Systems In Paradise
 IN PROC. IFAC SYMPOSIUM ON ROBUST CONTROL DESIGN
, 1997
"... Most of the methods which are commonly used in parametric oriented robust control design and analysis require extensive symbolic and numerical computations. The Matlab toolbox Paradise (PArametric Robustness Analysis and Design Interactive Software Environment) offers various methods of parametri ..."
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Cited by 3 (3 self)
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Most of the methods which are commonly used in parametric oriented robust control design and analysis require extensive symbolic and numerical computations. The Matlab toolbox Paradise (PArametric Robustness Analysis and Design Interactive Software Environment) offers various methods of parametric robust control for an efficient application in a computer framework. Amongst the currently implemented methods are the parameter space approach, design in an invariance plane, calculation of stability profiles, and computation of stability radii. The application of the toolbox Paradise is demonstrated by computation of stability radii for a state feedback controlled loading bridge.
Semialgebraic description of the equilibria of dynamical systems
"... Abstract. We study continuous dynamical systems defined by autonomous ordinary differential equations, themselves given by parametric rational functions. For such systems, we provide semialgebraic descriptions of their hyperbolic and nonhyperbolic equilibria, their asymptotically stable hyperbolic ..."
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Cited by 1 (1 self)
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Abstract. We study continuous dynamical systems defined by autonomous ordinary differential equations, themselves given by parametric rational functions. For such systems, we provide semialgebraic descriptions of their hyperbolic and nonhyperbolic equilibria, their asymptotically stable hyperbolic equilibria, their Hopf bifurcations. To this end, we revisit various criteria on sign conditions for the roots of a real parametric univariate polynomial. In addition, we introduce the notion of comprehensive triangular decomposition of a semialgebraic system and demonstrate that it is well adapted for our study. 1
Index Terms
"... A methodology to analyze robustness with respect to exogenous perturbations for exact feedforward linearization based on differential flatness is presented. The analysis takes into consideration the tracking error equation and makes thereafter use of a stability result by Kelemen coupled with result ..."
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A methodology to analyze robustness with respect to exogenous perturbations for exact feedforward linearization based on differential flatness is presented. The analysis takes into consideration the tracking error equation and makes thereafter use of a stability result by Kelemen coupled with results issued from interval analysis. This turns exact feedforward linearization based on differential flatness into a general control methodology for flat systems.
Design of Gain Scheduling Controllers in Parameter Space
, 1997
"... Up to now the parameter space approach was either utilized for robustness analysis or for design of fixed gain controllers. This paper presents an extension of this method which allows the design of gain scheduling controllers which simultaneously stabilize a finite number of representatives of an u ..."
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Up to now the parameter space approach was either utilized for robustness analysis or for design of fixed gain controllers. This paper presents an extension of this method which allows the design of gain scheduling controllers which simultaneously stabilize a finite number of representatives of an uncertain plant. The approach is applied to an automotive control example. 1 Introduction The parameter space approach can be used for design of controllers and robustness analysis of linear uncertain plants. In general, the approach requires a physically motivated modelling of the plant, i.e. the uncertain parameters have a physical relation, for example masses, lengths, etc. For convenience the uncertain parameters are gathered in q = [q 1 : : : q ` ] T , an uncertainty vector, where ` denotes the number of uncertain parameters. Each of the q i lies in an interval q i 2 [q \Gamma i ; q + i ]. In the case of independent uncertain parameters the uncertainty domain Q = fq i j q i 2 [q ...
PARADISE  PArametric Robust Analysis and Design Interactive Software Environment: A MatlabBased Robust Control Toolbox
"... This paper presents a new toolbox for robust control design and analysis. 1. Introduction The basis of robust control as it is considered in this paper is a physically motivated model of the plant, where the plant parameters q = [q 1 q 2 : : : q ` ] T enter into the system description. The depen ..."
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This paper presents a new toolbox for robust control design and analysis. 1. Introduction The basis of robust control as it is considered in this paper is a physically motivated model of the plant, where the plant parameters q = [q 1 q 2 : : : q ` ] T enter into the system description. The dependency of the system description on the uncertain parameters may be arbitrary, e.g. also nonlinear parameter dependency is possible. In general, the uncertain parameters are independent of each other and lie between upper and lower bounds. The uncertainty domain Q := fqj q i 2 [q \Gamma i ; q + i ]; i = 1; 2; : : : ; `g is then a hyperrectangle. As an example consider a model of a vehicle for automotive control, where the important parameters are load mL , velocity v, and road adhesion factor . All these parameters vary in given bounds. A system description, e.g. the linearized state space model, depends on these operating parameters [mL v ] T . For details on parametric modelling and...
Robust Control Goes PARADISE
, 1996
"... This paper presents a new toolbox for robust control design and analysis. 1 Introduction The basis of robust control as it is considered in this paper is a physically motivated model of the plant, where the plant parameters q = [q 1 q 2 . . . q # ] T enter into the system description. The depende ..."
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This paper presents a new toolbox for robust control design and analysis. 1 Introduction The basis of robust control as it is considered in this paper is a physically motivated model of the plant, where the plant parameters q = [q 1 q 2 . . . q # ] T enter into the system description. The dependency of the system description on the uncertain parameters may be arbitrary, e.g. also nonlinear parameter dependency is possible. In general, the uncertain parameters are independent of each other and lie between upper and lower bounds. The uncertainty domain Q := {q q i # [q  i ; q + i ], i = 1, 2, . . . , #} is then a hyperrectangle. As an example consider a model of a vehicle for automotive control, where the important parameters are load mL , velocity v, and road adhesion factor µ. All these parameters vary in given bounds. A system description, e.g. the linearized state space model, depends on these operating parameters [mL v µ] T . For details on parametric modelling and ...