John Tsinias

Sufficient lyapunov-like conditions for stabilization

In this paper we study the stabilizability problem for nonlinear control systems. We provide sufficient Lyapunov-like conditions for the possibility of stabilizing a control system at an equilibrium point of its state space. The stabilizing feedback laws are assumed to be smooth except possibly at the equilibrium point of the system.

Observer design for nonlinear control systems

Abstract This paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities. A sufficient Liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case.

A theorem on global stabilization of nonlinear systems by linear feedback

Abstract In this paper we investigate the global stabilizability problem for a wide class of single-input nonlinear systems whose the linearization at the equilirrium is controllable. We show that under general assumptions there exists a linear feedback law which globally exponentially stabilizes the system at its equilibrium. The proof of our main theorem is based on some ideas from a previous paper. We use the theorem to recover a recent result of Gauthier et al. concerning the observer design problem.

Further results on the observer design problem

Abstract In this paper the observer design problem for nonlinear systems is considered. Sufficient Lyapunov-like conditions are presented for the existence of a nonlinear observer. The theory we develop considerably improves and extends the results of our recent work [14].

Backstepping design for time-varying nonlinear systems with unknown parameters

Abstract A simple backstepping design procedure is proposed and sufficient conditions for global partial state- and dynamic- feedback stabilization for a class of triangular systems with unknown time-varying parameters are derived.

Sontag's “input to state stability condition” and global stabilization using state detection

This paper deals with the global stabilization problem for nonlinear system using state detection. Sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included. These conditions are based to a version of a Lyapunov-like condition proposed by Sontag, which guarantees ‘input to state stability’.

The concept of ‘Exponential input to state stability’ for stochastic systems and applications to feedback stabilization

Abstract This paper presents a version of the well-known Sontag’s ‘input-to-state-stability’ property for stochastic systems. This concept is used to derive sufficient conditions for global stabilization for certain class of stochastic nonlinear systems by means of static and dynamic output feedback.

Partial-state global stabilization for general triangular systems

Abstract We deal with the partial-state global stabilization problem for a wide class of nonlinear systems which contains those having triangular structure. The sufficient conditions we propose guarantee global stabilization by means of an output smooth feedback integrator.

Optimal controllers and output feedback stabilization

Abstract In this paper the output feedback stabilizability problem is explored in terms of control Lyapunov functions. Sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem. Our main results extends those developed in [31] and generalize a theorem due to Sontag [23].

A generalization of Vidyasagar's theorem on stability using state detection

In this paper we generalize the Vidyasagars well known theorem on the local stabilizability problem of nonlinear systems using state detection [11]. Our purpose is to prove that if a system is weakly detectable and stabilizable by means of a continuous state feedback u = γ(x), for which no differentiability assumption is imposed, then the system is also stabilized by the law u = γ(z), where z is the output of a weak detector for the state x. The result above is applicable to several cases not covered by other works.