The exponential stabilizability of switched nonlinear systems with polytopic uncertainties is explored by employing themethods of nonsmooth analysis and theminimum quadratic Lyapunov function. The switchings among subsystems are dependent on the directional derivative along the vertex directions of subsystems. In particular, a sufficient condition for exponential stabilizability of the switched...

Abstract The backstepping method is applied to a certain class of switched nonlinear systems to design state feedback controllers and a switching law based on multi-Lyapunov functions. The state feedback controllers and the switching law that can stabilize the system are developed. The switched nonlinear systems with uncertainties can be stabilized robustly by using the proposed method. Finally...

This paper studies switching stabilization problems for general switched nonlinear systems. A piecewise smooth controlLyapunov function (PSCLF) approach is proposed and a constructive way to design a stabilizing switching law is developed. The switching law is constructed via the directional derivatives of the PSCLF with a careful discussion on various technical issues that may occur on the non...

We address exponential stability of switched nonlinear singular systems with time-delay in which delay is time varying and presents in the states. For switched nonlinear singular time-delay systems with average dwell-time switching signals, we provide sufficient conditions, in terms of linear matrix inequalities (LMIs) to guarantee the exponential stability of such systems. By using Lyapunov–li...

Optimal control problems for switched nonlinear systems are investigated. We propose an alternative approach for solving the optimal control problem for a nonlinear switched system based on the theory of moments. The essence of this method is the transformation of a nonlinear, nonconvex optimal control problem, that is, the switched system, into an equivalent optimal control problem with linear...

The input-to-state stability (ISS) problem is studied for switched systems with infinite subsystems. By the method of multiple Lyapunov function, a sufficient ISS condition is given based on a quantitative relation of the input and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some suffic...

Zusammenfassung Es wird eine konstruktive Reglerentwurfsmethode für schaltende nichtlineare steuerungssaffine Systeme vorgestellt, die dem geschlossenen Regelkreis eine schaltende Port-Hamiltonsche Struktur mit gemeinsamer Energiefunktion zuweist und so (asymptotische) Stabilität der Ruhelage erzielt. Die Methode generiert alle schaltenden Zustandsrückführungen, welche die Strecke unter beliebi...

In this thesis, we deal with stability of uncertain positive systems. Although in recent years much attention has been paid to positive systems in general, there are still many areas that are left untouched. One of these areas, is the stability analysis of positive systems under any form of uncertainty. In this manuscript we study three broad classes of positive systems subject to different for...

SUMMARY The objective of this paper is to describe recent progress in the field of hybrid control of nonlinear systems. We address the problem of controlling a nonlinear dynamical process by means of an hybrid controller, i.e. a controller that combines continuous dynamics with discrete logics, the latter used to switch, from time to time, between several continuous controls laws. The hybrid co...

We focus on the development of a Lyapunov-based economic model predictive control (LEMPC) method for a class of switched nonlinear systems for which the mode transitions take place according to a prescribed switching schedule. In contrast to steady-state operation of conventional model predictive control (MPC) methods which use a quadratic objective function in their formulations, LEMPC utilize...