On exponential stabilizability of linear neutral systems.
On finite time stability with guaranteed cost control of uncertain linear systems
This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and the construction...
On generalized Popov theory for delay systems
This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoryless state feedback control law which guarantees the (exponential) closed-loop stability with an norm bound constraint on disturbance attenuation. Note that the proposed results extend...
On generic properties of linear systems: An overview
On -stability of autonomous systems.
On parametric Hurwitz stability margin of real polynomials
On Popov-type stability criteria for neural networks.
On practical stability and optimal stabilization of controlled motion
On quadratic Hurwitz forms. I
Homogeneous quadratic polynomials in complex variables are investigated and various necessary and sufficient conditions are given for to be nonzero in the set . Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.
On robust stability of neutral systems
This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems including some constant delays and time-varying cone-bounded nonlinearities. Sufficient stability conditions are derived by taking into account the weighting factors describing the nonlinearities. The proposed results are applied to the stability analysis of a class of lossless transmission line models.
On some relaxations commonly used in the study of linear systems
This note proposes a quite general mathematical proposition which can be a starting point to prove many well-known results encountered while studying the theory of linear systems through matrix inequalities, including the S-procedure, the projection lemma and few others. Moreover, the problem of robustness with respect to several parameter uncertainties is revisited owing to this new theorem, leading to LMI (Linear Matrix Inequality)-based conditions for robust stability or performance analysis...
On stabilizability of evolution systems of partial differential equations on ℝn×[0,+∞) by time-delayed feedback controlsby time-delayed feedback controls
On stable cones of polynomials via reduced Routh parameters
A problem of inner convex approximation of a stability domain for continuous-time linear systems is addressed in the paper. A constructive procedure for generating stable cones in the polynomial coefficient space is explained. The main idea is based on a construction of so-called Routh stable line segments (half-lines) starting from a given stable point. These lines (Routh rays) represent edges of the corresponding Routh subcones that form (possibly after truncation) a polyhedral (truncated) Routh...
On stable polynomials
The article is a survey on problem of the theorem of Hurwitz. The starting point of explanations is Schur's decomposition theorem for polynomials. It is showed how to obtain the well-known criteria on the distribution of roots of polynomials. The theorem on uniqueness of constants in Schur's decomposition seems to be new.
On sufficient conditions for the stability of dynamic interval systems
On the bounded input-bounded output stability of a second-order linear difference equation
On the characteristic polynomial of matrices with prescribed columns and the stabilization and observability of linear systems.
On the circle criterion for boundary control systems in factor form : Lyapunov stability and Lur’e equations
A Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur’e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on results...
On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations
A Lur'e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur'e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on...
On the controllability and stabilization of the linearized Benjamin-Ono equation
In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback law which...