Svyatoslav Pavlichkov

Global uniform input-to-state stabilization of large-scale interconnections of MIMO generalized triangular form switched systems

We solve the problem of global uniform input-to-state stabilization with respect to external disturbance signals for a class of large-scale interconnected nonlinear switched systems. The overall system is composed of switched subsystems each of which has the nonlinear MIMO generalized triangular form, which (in contrast to strict-feedback form) has non-invertible input–output maps. The switching signal is an arbitrary unknown piecewise constant function and the feedback constructed does not depend on the switching signal.

Global Stabilization of the Generalized MIMO Triangular Systems With Singular Input-Output Links

This work is devoted to the problem of global stabilization for a class of the general multi-input and multi-output (MIMO) triangular systems which are not feedback linearizable. To solve the problem, we develop a specific backstepping procedure and generalize some existing results. Since we deal with the global stabilization for the singular and MIMO case, the technique of the proof differs from the standard backstepping algorithms.

Robust Stabilization of the Generalized Triangular Form Nonlinear Systems With Disturbances

We investigate the problem of global uniform input-to-state stabilization of nonlinear generalized triangular form (GTF) control systems of ODE with time-varying and periodic dynamics and with external essentially bounded disturbances. Our first main result is a statement which is a kind of extension of theorems on “adding an integrator” to the case of input-to-state stabilization of GTF systems. As a corollary we immediately obtain our second main result on global uniform input-to-state stabilzation of GTF systems w.r.t. the external disturbances. The latter is a generalization of the recent result, devoted to the global asymptotic stabilization of the GTF systems without disturbances. It is essential that the proof of the main result is based on the converse ISS Lyapunov theorems for the time-varying systems, which allows to simplify construction proposed our recent work.

Uniform asymptotic stabilization of nonlinear switched systems with arbitrary switchings and with dynamic uncertainties by means of small gain theorems

The paper focuses on the problem of global uniform asymptotic stabilization of switched triangular form systems with unobservable dynamic uncertainties and with unknown switching signal. We prove that if the dynamic uncertainty is treated as external disturbance, then the triangular system can be stabilized with arbitrarily small gain w.r.t. the dynamic uncertainty. Then, using an extension of the well-known small gain theorem to the case of switched systems with arbitrary switchings, we obtain the uniform asymptotic stabilization of the overall interconnected system.

Constructive Design of Adaptive Controllers for Nonlinear MIMO Systems With Arbitrary Switchings

This technical note is devoted to the problem of global adaptive stabilization of switched triangular form systems with unknown parameters. The switching signal is assumed to be unknown and the input-output maps of the triangular form are assumed to be right-invertible. A scheme to find a stabilizing controller is provided.

A new small gain theorem for large-scale networks of switched systems with arbitrary switchings

We consider a large-scale switched nonlinear system which is composed as an interconnection of N nonlinear switched systems. Having assumed that every subsystem is ISpS (ISS) uniformly with respect to the unobservable switching signals, we prove a small-gain condition for the overall large-scale system to be ISpS (respectively ISS) uniformly with respect to the unknown switching signal. To solve the problem we extend the well-known result by E.D. Sontag and Y. Wang on characterizations of input-to-state stability property to the case of uniform ISS of switched systems with arbitrary switchings.

Uniform Stabilization of Nonlinear Systems With Arbitrary Switchings and Dynamic Uncertainties

We solve the problem of global uniform input-to-state stabilization of nonlinear switched systems with time-varying and periodic dynamics, with dynamic uncertainties, and with external disturbances. The switching signal is assumed to be unknown and the dynamics of the known components of the state vector is equivalent to the general triangular form (GTF) with non-invertible input-output maps. In our first and most general result, we prove that, if the dynamic uncertainty is treated as external disturbance, then the general triangular form system can be stabilized with arbitrarily small gain w.r.t. the dynamic uncertainty by means of a switching-independent, smooth and periodic feedback. Hence, using a suitable extension of the well-known small gain theorem to our case of switched systems with arbitrary switchings, we obtain the uniform input-to-state stabilization of the entire interconnected system. The second part of the paper addresses a more special case of triangular form (TF) switched systems with right-invertible input-output (I-O) maps with unknown switchings and with dynamic uncertainties. We show that the design becomes simpler and more constructive and the controllers become time-invariant if the dynamics is autonomous in this special case. Finally, we consider an example with explicit design of the stabilizing controllers.

Stabilization of Generalized Triangular Form Systems with Dynamic Uncertainties by Means of Small Gain Theorems

Abstract We prove that a nonlinear control system with periodic dynamics in the generalized triangular form (GTF) which is affected by external disturbances can be uniformly input-to-state stabilized by means of a periodic feedback and the gain can be chosen arbitrarily small in some sense. This allows us to stabilize such a system in presence of unmeasured dynamic uncertainties.

Design of adaptive controllers for nonlinear switched systems with arbitrary switchings

This note is devoted to the problem of global adaptive stabilization of switched triangular form systems with unknown parameters. The switching signal is assumed to be unknown and the input-output maps of the triangular form are assumed to be right-invertible. A scheme to find a stabilizing controller is provided.