Invariance Principles and Observability in Switched Systems with an Application in Consensus

Using any nonnegative function with a nonpositive derivative along trajectories to define a virtual output, the classic LaSalle invariance principle can be extended to switched nonlinear time-varying (NLTV) systems, by considering the weak observability (WO) associated with this output. WO is what the output informs about the limiting behavior of state trajectories (hidden in the zero locus of the output). In the context of switched NLTV systems, WO can be explored using the recently established framework of limiting zeroing-output solutions. Adding to this, an extension of the integral invariance principle for switched NLTV systems with a new method to guarantee uniform global attractivity of a closed set (without assuming uniform Lyapunov stability or dwell-time conditions) is proposed. By way of illustrating the proposed method, a leaderless consensus problem for nonholonomic mobile robots with a switching communication topology is addressed, yielding a new control strategy and a new convergence result

Invariance principles for switched systems with restrictions

In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe

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

Geometrical Lorentz Violation and Quantum Mechanical Physics

On the basis of the results of some experiments dealing with the violation of Local Lorentz Invariance (LLI) and on the formalism of the Deformed Special Relativity (DSR), we examine the connections between the local geometrical structure of space-time and the foundation of Quantum Mechanics. We show that Quantum Mechanics, beside being an axiomatic theory, can be considered also a deductive physical theory, deducted from the primary physical principle of Relativistic Correlation. This principle is synonym of LLI and of a rigid and at minkowskian space-time. The results of the experiments mentioned above show the breakdown of LLI and hence the violation of the principle of Relativistic Correlation. The formalism of DSR allows to highlight the deep meaning of LLI breakdown in terms of the geometrical structure of local space-time which, far from being rigid and at, is deformed by the energy of the physical phenomena that take place and in this sense it has an active part in the dynamics of the whole physical process. This perspective has a far reaching physical meaning that extends its consequences to the foundations of Quantum Mechanics according to the interpretation of Copenhagen. It provides a 'real' explanation and description of quantum phenomena enriching, by the concept of deformed space-time, the realistic interpretation in terms of pilot wave and hence it uncovers the reality hidden below the probabilistic interpretation and dualistic nature of quantum objects.Comment: 4 figures, 15 page