Minimum Dwell Times for the Stability of Switched Systems with Multiple Stable Operating Points

Sufficient conditions for the stability of linear-switched systems with dwell-time and polytopic-type parameter uncertainties are presented. A Lyapunov function, in quadratic form, which is nonincreasing at the switching instants is assigned to each subsystem. During the dwell time, this function varies piecewise linearly in time after switching occurs and it becomes time invariant afterward. This function leads to asymptotic stability conditions for the nominal set of the subsystems that can be readily extended to the case where these subsystems suffer from polytopic-type parameter uncertainties. The method proposed is then applied to stabilization via state feedback, both for the nominal and the uncertain cases.

Gene regulatory networks (GRNs) perform a pivotal task in conducting cellular functions. Reconstruction of these complex networks is necessary to understand underlying mechanisms directing cellular behavior. This paper deals with structure identification for gene regulatory networks. To do this end, adaptive observer is employed to estimate unknown parameters. In this method, convergence of parameter estimation to the true values depends on persistency of excitation condition. Since many real gene networks don't satisfy this condition, we propose a new method to derive these parameters. This approach is based on introducing a switching mechanism in gene networks by using biochemical perturbations. Moreover, an adaptive observer for switching systems is designed and sufficient conditions for convergence of its parameters are derived based on stability of switching systems. Proposed adaptive observer provide exponential convergence of parameters estimation and switching mechanism improve persistency of excitation. By several simulations, it is shown that the proposed method indicates better performance in contrast to the existing methods for structure identification. Regarding the obtained results, our method leads to faster convergence, handles larger unknown parameter cases and estimates true values while other methods fail.

Path-complete methods utilize a set of positive definite functions and a specially constructed graph in order to evaluate, among others, stability of switching systems. This tool is shown to be general, e.g., path-complete criteria are universal for linear switching systems and quadratic templates. In this work, we extend the approach to polyhedral Lyapunov functions, and introduce a simple parameterization that can be sufficient for stability analysis. Moreover, we indicate ways of obtaining less conservative stability criteria by partial graph extensions, all evaluated by solving Linear Programs (LPs).

Stability and stabilizability of discrete-time dual switching systems with application to sampled-data systems

Ensuring constraint satisfaction is distinctly challenging for externally switched systems. Previous work addressing these challenges has focused on cases where the time between switches is longer than some minimum dwell time. While this admits assurances of feasibility, it precludes uncontrollable modes. Further, the presence of poorly behaved modes, where the control actions only narrowly overcome instability, can greatly decrease the size of the switched system's persistently feasible regions. To surmount these issues, this work examines systems with transient modes that will only be active for some maximum dwell time. Corresponding feasible regions, represented by safe-sets are developed that make use of these transient modes. Not only does this permit feasibility assurances in systems with uncontrollable modes, but this also limits the impact poorly behaving modes. These benefits are demonstrated in two numerical examples. Further, the implementation of these results in model predictive control is discussed.

This work researches the problem of searching for multiple homogeneous polynomial Lyapunov functions (HPLFs) for heterogeneous switched linear systems. First, a nonconvex optimization condition is constructed to study the stability property of heterogeneous switched systems, where each Lyapunov function candidate reduces dimension to their corresponding matrix eigenvalue. Based on the stability analysis condition, a controller-dependently multiple HPLFs condition is introduced to determine controllers and explores locally minimum mode-dependent average dwell time (LMMDADT). Additionally, the existing properties condition and solvable properties condition of controllers are given in the form of HPLFs. At last, a practical example and a contrast example are both presented to show feasibility of the proposed results.

We describe a new class of positive linear discrete-time switching systems for which the problems of stability or stabilizability can be resolved constructively. The systems constituting this class can be treated as a natural generalization of systems with the so-called independently switching state vector components. Distinctive feature of such systems is that their components can be arbitrarily “re-connected” in parallel or in series without loss of the “constructive resolvability” property for the problems of stability or stabilizability of a system. It is shown also that, for such systems, the individual positive trajectories with the greatest or the lowest rate of convergence to the zero can be built constructively.

We consider a plant switching among a set of dynamic systems each associated with a single stable equilibrium point. We assume that a constraint region for the state is assigned. The main problem is that of finding suitable limitations on the commutation speed in order to avoid constraints violations, even in the absence of state measurements. We introduce the concepts of modal and transition dwell times which lead to a dwell time vector and dwell time graph (represented by a proper matrix), respectively. The former imposes a minimum permanence on a discrete mode before commuting, the second imposes the minimum permanence on the current mode before switching to a specific new one. Both dwell time vector and dwell time graph, can be computed via set theoretic techniques. When systems share a single equilibrium stability can be assured as a special case. Finally, under the assumption of affine dynamics, non-conservative values are achieved.

In this paper a switching controller for mobile robots is presented that allows the contour-following of objects the size of which is at least comparable to that of the robot. The controller uses the information from distance sensors and is based on a wall-following controller described in the paper. The stability of the overall switching system is proved by using a common Lyapunov function. Experimental results in a Pioneer III unicycle-like mobile robot are provided to show the feasibility of the proposed control strategy

This paper is concerned with the problem of robust stabilization for a class of uncertain two-dimensional (2D) discrete switched systems with state delays under asynchronous switching. The asynchronous switching here means that the switching instants of the controller experience delays with respect to those of the system. The parameter uncertainties are assumed to be norm-bounded. A state feedback controller is proposed to guarantee the exponential stability. The dwell time approach is utilized for the stability analysis and controller design. A numerical example is given to illustrate the effectiveness of the proposed method.

This paper describes a geometric procedure, whose aim is to provide necessary and sufficient conditions for the stability of a class of planar switching systems against arbitrary switching. The main idea is to build the worst switching sequence and to exploit it to get information about the stability for every switching sequence. The analysis is conveyed initially for LTI subsystems, then it is extended to homogeneous subsystems of the same degree having the origin as the unique equilibrium point. Finally, a simple method to build suitable Lyapunov functions to verify the stability of such systems is provided.

The U.S. Department of Energy (DOE) and the U.S. Council for Automotive Research (composed of automakers Ford, General Motors, and Chrysler) announced in January 2002 a new cooperative research effort. Known as FreedomCAR (derived from 'Freedom' and 'Cooperative Automotive Research'), it represents DOE's commitment to developing public/private partnerships to fund high-risk, high-payoff research into advanced automotive technologies. Efficient fuel cell technology, which uses hydrogen to power automobiles without air pollution, is a very promising pathway to achieve the ultimate vision. The new partnership replaces and builds upon the Partnership for a New Generation of Vehicles initiative that ran from 1993 through 2001. The Advanced Power Electronics and Electric Machines (APEEM) subprogram within the Vehicle Technologies Program provides support and guidance for many cutting-edge automotive technologies now under development. Research is focused on understanding and improving the way the various new components of tomorrow's automobiles will function as a unified system to improve fuel efficiency. In supporting the development of hybrid propulsion systems, the APEEM effort has enabled the development of technologies that will significantly improve advanced vehicle efficiency, costs, and fuel economy. The APEEM subprogram supports the efforts of the FreedomCAR and Fuel Partnership through a three-phase approach intended to: (1) identify overall propulsion and vehicle-related needs by analyzing programmatic goals and reviewing industry's recommendations and requirements and then develop the appropriate technical targets for systems, subsystems, and component research and development activities; (2) develop and validate individual subsystems and components, including electric motors, and power electronics; and (3) determine how well the components and subsystems work together in a vehicle environment or as a complete propulsion system and whether the efficiency and performance targets at the vehicle level have been achieved. The research performed under this subprogram will help remove technical and cost barriers to enable the development of technology for use in such advanced vehicles as hybrid electric vehicles (HEVs), plug-in HEVs, and fuel-cell-powered automobiles that meet the goals of the Vehicle Technologies Program. A key element in making HEVs practical is providing an affordable electric traction drive system. This will require attaining weight, volume, and cost targets for the power electronics and electrical machines subsystems of the traction drive system. Areas of development include these: (1) novel traction motor designs that result in increased power density and lower cost; (2) inverter technologies involving new topologies to achieve higher efficiency and the ability to accommodate higher-temperature environments; (3) converter concepts that employ means of reducing the component count and integrating functionality to decrease size, weight, and cost; (4) more effective thermal control and packaging technologies; and (5) integrated motor/inverter concepts. The Oak Ridge National Laboratory's (ORNL's) Power Electronics and Electric Machinery Research Center conducts fundamental research, evaluates hardware, and assists in the technical direction of the DOE Vehicle Technologies Program, APEEM subprogram. In this role, ORNL serves on the FreedomCAR Electrical and Electronics Technical Team, evaluates proposals for DOE, and lends its technological expertise to the direction of projects and evaluation of developing technologies.

Dwelling time probability density distribution of instances in a workflow model

This article concentrates on the output feedback controller design problem for discrete-time nonlinear switched systems with actuator faults. The Takagi-Sugeno fuzzy model is adopted to approximate the nonlinearity of the plant with a set of local linear models. The persistent dwell-time (DT) switching law, which is more general than DT or average DT switching, is introduced to govern the switching among subsystems. In order to alleviate the effects of actuator failures on system stability and performance, a synthesized fault-tolerant output feedback controller ensuring various performance requirements is designed. Intensive attention is focused on establishing sufficient conditions, which can guarantee the exponential mean-square stability as well as the prescribed extended dissipativity property of the closed-loop system. By virtue of the Lyapunov stability theory and appropriate matrix transformation methods, the desired controller gains can be obtained by solving a convex optimization problem. The developed method is finally applied to address the control issue of a tunnel diode circuit system model to illustrate its efficiency and applicability.

This paper mainly investigates the state constrained switched system with fully unstable subsystems. By limiting the state in a unit hypercube, a sufficient condition is derived to ensure the stability of such systems via a time-dependent strategy. The main idea is to use positive switching behavior to compensate state divergence caused by unstable states and setting a different ascend rate when state constraints occur or not. In order to make the conditions computable for a continuous-time switched systems with state constraints, the discretized Lyapunov Function method is applied, then a numerical example is given to show the practicability of the proposed method.