Convergence Rate of Nonlinear Switched Systems

This paper is concerned with the convergence rate of the solutions of nonlinear switched systems. We first consider a switched system which is asymptotically stable for a class of inputs but not for all inputs. We show that solutions corresponding to that class of inputs converge arbitrarily slowly to the origin. Then we consider analytic switched systems for which a common weak quadratic Lyapunov function exists. Under two different sets of assumptions we provide explicit exponential convergence rates for inputs with a fixed dwell-time

Large-signal stability conditions for semi-quasi-Z-source inverters: switched and averaged models

The recently introduced semi-quasi-Z-source in- verter can be interpreted as a DC-DC converter whose input- output voltage gain may take any value between minus infinity and 1 depending on the applied duty cycle. In order to generate a sinusoidal voltage waveform at the output of this converter, a time-varying duty cycle needs to be applied. Application of a time-varying duty cycle that produces large-signal behavior requires careful consideration of stability issues. This paper provides stability results for both the large-signal averaged and the switched models of the semi-quasi-Z-source inverter operating in continuous conduction mode. We show that if the load is linear and purely resistive then the boundedness and ultimate boundedness of the state trajectories is guaranteed provided some reasonable operation conditions are ensured. These conditions amount to keeping the duty cycle away from the extreme values 0 or 1 (averaged and switched models), and limiting the maximum PWM switching period (switched model). The results obtained can be used to give theoretical justification to the inverter operation strategy recently proposed by Cao et al. in [1].Comment: Submitted to the IEEE Conf. on Decision and Control, Florence, Italy, 201

Stability of uniformly bounded switched systems and Observability

This paper mainly deals with switched linear systems defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function. Its aim is to give sufficient conditions for such a system to be GUAS.We show that this property of being GUAS is equivalent to the uniform observability on $[0,+\infty)$ of a bilinear system defined on a subspace whose dimension is in most cases much smaller than the dimension of the switched system.Some sufficient conditions of uniform asymptotic stability are then deduced from the equivalence theorem, and illustrated by examples.The results are partially extended to nonlinear analytic systems

Asymptotic Behavior of a Class of Evolution Variational Inequalities

We establish a new LaSalle's invariance principle and discuss the asymptotic behavior of a class of first-order evolution variational inequalities

On reduction of differential inclusions and Lyapunov stability

In this paper, locally Lipschitz, regular functions are utilized to identify and remove infeasible directions from set-valued maps that define differential inclusions. The resulting reduced set-valued map is point-wise smaller (in the sense of set containment) than the original set-valued map. The corresponding reduced differential inclusion, defined by the reduced set-valued map, is utilized to develop a generalized notion of a derivative for locally Lipschitz candidate Lyapunov functions in the direction(s) of a set-valued map. The developed generalized derivative yields less conservative statements of Lyapunov stability theorems, invariance theorems, invariance-like results, and Matrosov theorems for differential inclusions. Included illustrative examples demonstrate the utility of the developed theory

Switched systems with multiple invariant sets

This paper explores dwell time constraints on switched systems with multiple, possibly disparate invariant limit sets. We show that, under suitable conditions, trajectories globally converge to a superset of the limit sets and then remain in a second, larger superset. We show the effectiveness of the dwell-time conditions by using examples of switching limit cycles commonly found in robotic locomotion and flapping flight