Pierre-alexandre Bliman

Convergence speed of unsteady distributed consensus: decay estimate along the settling spanning-trees (2006)

The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of...

Stability of leaderless multi-agent systems. Extension of a result by Moreau (2005)

Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information...

Average consensus problems in networks of agents with delayed communications (2005)

The paper presents a result which relates connectedness of the interaction graphs in a multi-agent systems with the capability for global convergence to a common equilibrium of the system. In...

Bliman, Pierre-Alexandre, Ferrari-Trecate, Giancarlo

The present paper is devoted to the study of average consensus problems for undirected networks of dynamic agents having communication delays. The accent is put here on the study of the time-delays...

Stability of leaderless multi-agent systems. Extension of a result by Moreau (2004)

Stability of leaderless multi-agent systems. Extension of a result by Moreau (2004)

The paper presents a result which relates connectedness of the interaction graphs in a multi-agent systems with the capability for global convergence to a common equilibrium of the system. In...

Stability of leaderless multi-agent systems. Extension of a result by Moreau (2004)

The paper presents a result which relates connectedness of the interaction graphs in a multi-agent systems with the capability for global convergence to a common equilibrium of the system. In...

On Positiveness of Matrix-Valued Polynomials and Robust Semidefinite Programming (2003)

The paper presents a result which relates connectedness of the interaction graphs in a multi-agent systems with the capability for global convergence to a common equilibrium of the system. In...

Existence of Polynomial Solutions to Robust Convex Programming Problems (2003)

This report is devoted to the study of robust semidefinite programming. We show that to the issue of computing the worst-case optimal value of semidefinite programs depending polynomially upon a...

An existence result for polynomial solutions of parameter-dependent LMIs (2003)

We show in this note that, under general conditions, any convex programming problem depending continuously upon scalar parameters, and solvable for any value of the latter in a fixed compact set,...

On Positiveness of Matrix-Valued Polynomials and Robust Semidefinite Programming (2003)

We show in this report that any system of Linear Matrix Inequalities depending continuously upon scalar parameters and solvable for any value of the latter in a fixed compact set, admits a branch of...

Existence of Polynomial Solutions to Robust Convex Programming Problems (2003)

This report is devoted to the study of robust semidefinite programming. We show that to the issue of computing the worst-case optimal value of semidefinite programs depending polynomially upon a...

An existence result for polynomial solutions of parameter-dependent LMIs (2003)

We show in this note that, under general conditions, any convex programming problem depending continuously upon scalar parameters, and solvable for any value of the latter in a fixed compact set,...

On Positiveness of Matrix-Valued Polynomials and Robust Semidefinite Programming (2003)

We show in this report that any system of Linear Matrix Inequalities depending continuously upon scalar parameters and solvable for any value of the latter in a fixed compact set, admits a branch of...

Existence of Polynomial Solutions to Robust Convex Programming Problems (2003)

This report is devoted to the study of robust semidefinite programming. We show that to the issue of computing the worst-case optimal value of semidefinite programs depending polynomially upon a...

An existence result for polynomial solutions of parameter-dependent LMIs (2003)

We show in this note that, under general conditions, any convex programming problem depending continuously upon scalar parameters, and solvable for any value of the latter in a fixed compact set,...

Control of delay systems with relay (2002)

We show in this report that any system of Linear Matrix Inequalities depending continuously upon scalar parameters and solvable for any value of the latter in a fixed compact set, admits a branch of...

Akian, Marianne, Bliman, Pierre-Alexandre, Sorine, Michel

We study the periodic oscillations of a first‐order delayed linear system with relay output and proportional + integral feedback and describe the behaviour of the general solutions of the...

A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters (2001)

Nonconservative LMI Criteria for Characterization of Delay-Independent Properties of Delay Systems. Application to Stability and Input-Output Analysis of Systems with Complex Parameter (2001)

In this report, robust stability for linear systems with several uncertain (complex and/or real) scalar parameters, is studied. Necessary and sufficient conditions for robust stability are given, in...

Lyapunov Equation for the Stability of Linear Delay Systems of Retarded and Neutral Type (2001)

This report focuses on delay-independent stability and delay-independent input-output properties (passivity, $H_\infty$ performance, circle criterion, Popov criterion) of delay systems. The main...

A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters (2001)

In this note is studied the delay-independent stability of delay systems. It is shown that the strong delay-independent stability is tantamount to the feasibility of certain linear matrix inequality,...

Nonconservative LMI Criteria for Characterization of Delay-Independent Properties of Delay Systems. Application to Stability and Input-Output Analysis of Systems with Complex Parameter (2001)

In this report, robust stability for linear systems with several uncertain (complex and/or real) scalar parameters, is studied. Necessary and sufficient conditions for robust stability are given, in...

Lyapunov Equation for the Stability of Linear Delay Systems of Retarded and Neutral Type (2001)

This report focuses on delay-independent stability and delay-independent input-output properties (passivity, $H_\infty$ performance, circle criterion, Popov criterion) of delay systems. The main...

A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters (2001)

In this note is studied the delay-independent stability of delay systems. It is shown that the strong delay-independent stability is tantamount to the feasibility of certain linear matrix inequality,...

Nonconservative LMI Criteria for Characterization of Delay-Independent Properties of Delay Systems. Application to Stability and Input-Output Analysis of Systems with Complex Parameter (2001)

In this report, robust stability for linear systems with several uncertain (complex and/or real) scalar parameters, is studied. Necessary and sufficient conditions for robust stability are given, in...

Lyapunov Equation for the Stability of Linear Delay Systems of Retarded and Neutral Type (2001)

This report focuses on delay-independent stability and delay-independent input-output properties (passivity, $H_\infty$ performance, circle criterion, Popov criterion) of delay systems. The main...

Lyapunov Equation for the Stability of 2-D Systems (2000)

In this note is studied the delay-independent stability of delay systems. It is shown that the strong delay-independent stability is tantamount to the feasibility of certain linear matrix inequality,...

LMI characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov-Krasovskii functionals (2000)

In this report, an analogue of the characterization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation is proposed for 2-D systems. It is shown that...

Stability of nonlinear delay systems : delay-independent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method (2000)

In this note is proposed an analogue for linear delay systems of the character- ization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation. It is shown...

Lyapunov Equation for the Stability of 2-D Systems (2000)

The purpose of this note is to study the relationship between a certain stability criterion for nonlinear delay systems, obtained via Lyapunov-Krasovs- kii method, and a delay-independent version of...

LMI characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov-Krasovskii functionals (2000)

In this report, an analogue of the characterization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation is proposed for 2-D systems. It is shown that...

Stability of nonlinear delay systems : delay-independent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method (2000)

In this note is proposed an analogue for linear delay systems of the character- ization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation. It is shown...

Lyapunov Equation for the Stability of 2-D Systems (2000)

The purpose of this note is to study the relationship between a certain stability criterion for nonlinear delay systems, obtained via Lyapunov-Krasovs- kii method, and a delay-independent version of...

LMI characterization of the strong delay-independent stability of linear delay systems via quadratic Lyapunov-Krasovskii functionals (2000)

In this report, an analogue of the characterization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation is proposed for 2-D systems. It is shown that...

Stability of nonlinear delay systems : delay-independent small gain theorem and frequency domain interpretation of the Lyapunov-Krasovskii method (2000)

In this note is proposed an analogue for linear delay systems of the character- ization of asymptotic stability of the rational systems by the solvability of associated Lyapunov equation. It is shown...

Extension of Popov Absolute Stability Criterion to Nonautonomous Systems with Delays (1999)

The purpose of this note is to study the relationship between a certain stability criterion for nonlinear delay systems, obtained via Lyapunov-Krasovs- kii method, and a delay-independent version of...

Extension of Popov Absolute Stability Criterion to Nonautonomous Systems with Delays (1999)

This paper extends in a simple way the classical absolute stability Popov criterion to multivariable systems with delays and with time-varying memoryles- s nonlinearities subject to sector...

Extension of Popov Absolute Stability Criterion to Nonautonomous Systems with Delays (1999)

This paper extends in a simple way the classical absolute stability Popov criterion to multivariable systems with delays and with time-varying memoryles- s nonlinearities subject to sector...

An Extension of Popov Criterion to Multivariable Time-Varying Nonlinear Systems. Application to Criterion for Existence of Stable Limit Cycles (1998)

This paper extends in a simple way the classical absolute stability Popov criterion to multivariable systems with delays and with time-varying memoryles- s nonlinearities subject to sector...

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M.

This report deals with sufficient conditions for absolute stability of multivariable control systems. The proposed conditions extend in a simple way the classical Popov criterion to time-varying...

An Extension of Popov Criterion to Multivariable Time-Varying Nonlinear Systems. Application to Criterion for Existence of Stable Limit Cycles (1998)

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M.

This report deals with sufficient conditions for absolute stability of multivariable control systems. The proposed conditions extend in a simple way the classical Popov criterion to time-varying...

On Super-High-Frequencies in Discontinuous 1st-Order Delay-Differential Equations (1998)

Akian, Marianne, Bliman, Pierre-Alexandre

One considers a scalar 1st-order nonlinear differential equation with a delayed relay-output proportional feedback. One shows that, under a boundedness condition on the nonlinearity only, any...

P.I. Control of Nonlinear Oscillations for a System with Delay (1998)

Akian, Marianne, Bliman, Pierre-Alexandre, Sorine, Michel

We study the periodic oscillations of a 1st order delayed linear system with relay output and proportional$+$integral feedback and describe the behavior of the general solutions of the closed loop....

An Extension of Popov Criterion to Multivariable Time-Varying Nonlinear Systems. Application to Criterion for Existence of Stable Limit Cycles (1998)

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M.

This report deals with sufficient conditions for absolute stability of multivariable control systems. The proposed conditions extend in a simple way the classical Popov criterion to time-varying...

On Super-High-Frequencies in Discontinuous 1st-Order Delay-Differential Equations (1998)

Akian, Marianne, Bliman, Pierre-Alexandre

One considers a scalar 1st-order nonlinear differential equation with a delayed relay-output proportional feedback. One shows that, under a boundedness condition on the nonlinearity only, any...

P.I. Control of Nonlinear Oscillations for a System with Delay (1998)

Akian, Marianne, Bliman, Pierre-Alexandre, Sorine, Michel

We study the periodic oscillations of a 1st order delayed linear system with relay output and proportional$+$integral feedback and describe the behavior of the general solutions of the closed loop....

Nonlinear Resonance in Systems with Hysteresis (1996)

Pierre-Alexandre Bliman, Alexander A. Vladimirov, Re Bliman, Re Bliman, Alexander M. Krasnosel'skii, Er M. Krasnosel'skii, ...

: A general approach is suggested for the analysis of nonlinear resonance in control systems including an integral linear term and a nonlinear term with hysteresis. This approach uses a special...

Nonlinear Resonance in Systems with Hysteresis (1995)

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M., Sorine, Michel, Vladimirov, Alexander A.

A general approach is suggested for the analysis of nonlinear resonance in control systems including an integral linear term and a nonlinear term with hysteresis. This approach uses a special...

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M., Sorine, Michel

This paper deals with differential inclusion containing an hysteresis nonlinearity and two inputs: a control input and a dither input of high frequency. Conditions are introduced under which its...

Nonlinear Resonance in Systems with Hysteresis (1995)

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M., Sorine, Michel, Vladimirov, Alexander A.

A general approach is suggested for the analysis of nonlinear resonance in control systems including an integral linear term and a nonlinear term with hysteresis. This approach uses a special...

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M., Sorine, Michel

This paper deals with differential inclusion containing an hysteresis nonlinearity and two inputs: a control input and a dither input of high frequency. Conditions are introduced under which its...

Nonlinear Resonance in Systems with Hysteresis (1995)

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M., Sorine, Michel, Vladimirov, Alexander A.

A general approach is suggested for the analysis of nonlinear resonance in control systems including an integral linear term and a nonlinear term with hysteresis. This approach uses a special...

Bliman, Pierre-Alexandre, Krasnosel'Skii, Alexander M., Sorine, Michel

This paper deals with differential inclusion containing an hysteresis nonlinearity and two inputs: a control input and a dither input of high frequency. Conditions are introduced under which its...