Browsing by Subject "Switched systems"

Now showing 1 - 10 of 10

Open Access
Conditions of well-posedness for planar conewise linear systems
(Sage Publications, 2023-04-24) Namdar, Daniyal; Özgüler, Arif Bülent
A planar (2D) conewise linear system (CLS) is considered. This is a piecewise linear system of two states and multiple modes, where each mode is linear with its state-space constrained into a polyhedral, finitely generated, convex cone. It is allowed to have a discontinuous vector field and sliding modes. Alternative conditions for well-posedness of Caratheodory solutions of this system that have intuitive interpretations with respect to eigenvectors and cone-boundary vectors are derived. It is also shown that a well-known condition for well-posedness of bimodal systems also applies to two adjacent modes of this system without any change.
Open Access
Dwell time-based stabilisation of switched linear delay systems using clock-dependent Lyapunov-Krasovskii functionals
(Taylor and Francis, 2018) Koru, A. T.; Delibaşı, A.; Özbay, Hitay
Dwell time stability conditions of the switched delay systems are derived using multiple clock-dependent Lyapunov-Krasovskii functionals. The corresponding conditions are approximated by both using piecewise linear functions and sum of squares polynomials. The upper bound of the dwell time is minimised using a combination of a bisection and a golden section search algorithm. Using the results obtained in the stability case, synthesis of dwell time minimiser controllers are presented. Some numerical examples are given to illustrate effectiveness of the proposed method, and its performance is compared with the existing approaches. The resulting values of the dwell time via the proposed technique show that the novel approach outperforms the previous ones.
Open Access
Dynamic output feedback stabilization of switched linear systems with delay via a trajectory based approach
(Elsevier, 2018) Ahmed, Saeed; Mazenc, F.; Özbay, Hitay
A new technique is proposed to construct observers and to achieve output feedback stabilization of a class of continuous-time switched linear systems with a time-varying delay in the output. The delay is a piecewise continuous bounded function of time and no constraint is imposed on the delay derivative. For stability analysis, an extension of a recent trajectory based approach is used; this is fundamentally different from classical Lyapunov function based methods. A stability condition is given in terms of the upper bound on the time-varying delay to ensure global uniform exponential stability of the switched feedback system. The main result applies in cases where some of the subsystems of the switched system are not stabilizable and not detectable.
Open Access
On dwell time minimization for switched delay systems: free-weighting matrices method
(IEEE, 2014) Koru, A. T.; Delibaşı, A.; Özbay, Hitay
In this paper, we present a quasi-convex minimization method to calculate an upper bound of dwell-time for stability of switched delay systems. Piecewise Lyapunov-Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals are estimated by free weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for dwell-time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities (LMIs), dwell time optimization problem can be formulated as a standard quasi-convex optimization problem. Numerical examples are given to illustrate improvements over previously obtained dwell-time bounds.
Open Access
On dwell time minimization for switched delay systems: Time-Scheduled Lyapunov Functions
(Elsevier B.V., 2016) Koru, A. T.; Delibaşı, A.; Özbay, Hitay
In the present paper, dwell time stability conditions of the switched delay systems are derived using scheduled Lyapunov-Krasovskii functions. The derivative of the Lyapunov functions are guaranteed to be negative semidefinite using free weighting matrices method. After representing the dwell time in terms of linear matrix inequalities, the upper bound of the dwell time is minimized using a bisection algorithm. Some numerical examples are given to illustrate effectiveness of the proposed method, and its performance is compared with the existing approaches. The yielding values of dwell time via the proposed technique show that the novel approach outperforms the previous ones. © 2016
Open Access
Stability analysis of switched systems using Lyapunov-Krasovskii functionals
(Elsevier, 2011) Çalişkan, S.Y.; Özbay, Hitay; Niculescu, S.-I.
Piecewise Lyapunov-Razumikhin functions are previously used for obtaining a lower bound for the dwell time of the switched time delay systems under the assumption that each candidate system is delay dependently stable. In this work, using Lyapunov-Krasovskii functionals, a less conservative lower bound for the dwell time is obtained. Improvement in the dwell time is illustrated with an example. © 2011 IFAC.
Open Access
Stability analysis of switched systems with time-varying discontinuous delays
(IEEE, 2017) Mazenc, F.; Malisoff, M.; Özbay, Hitay
A new technique is proposed to ensure global asymptotic stability for nonlinear switched time-varying systems with time-varying discontinuous delays. It uses an adaptation of Halanay's inequality to switched systems and a recent trajectory based technique. The result is applied to a family of linear time-varying systems with time-varying delays.
Open Access
Stability of third order conewise linear systems
(2019-07) Zakwan, Muhammad
A conewise linear, time-invariant system is a piecewise linear system in which the state-space is a union of polyhedral cones. Each cone has its own dynamics so that a multi-modal system results. We focus our attention to global asymptotic stability so that each mode (or subsystem) is autonomous. i.e., driven only by initial states. Conewise linear systems are of great relevance from both practical and theoretical point of views as they represent an immediate extension of linear, time-invariant systems. A clean and complete necessary and sufficient condition for stability of this class of systems has been obtained only when the cones are planar, that is only when the state space is R2. This thesis is devoted to the case of state-space being R3, although occasionally we also consider the general case Rn. We aim to determine conditions for stability exploring the geometry of the modes. Thus our results do not make use of a Lyapunov function based approach for stability analysis. We first consider an individual mode and determine whether a cone with a given dynamics can be classified as a sink, source, or transitive from one or two borders. It turns out that the classification not only depends on the geometry of the eigenvectors and the geometry of the cone but also on entries of the A-matrix that defines the dynamics. Under suitable assumptions on the configuration of the eigenvectors relative to the cone, we manage to obtain relatively clean charecterizations for transitive modes. Combining this with a complete characterization of sinks and sources, we use some tools from graph theory and obtain an interesting sufficient condition for stability of a conewise system composed of transitive modes, sources, and sinks. Finally, we apply our results to study the stability of a linear RC electrical network containing diodes.
Open Access
State feedback stabilization of switched systems with delay: trajectory based approach
(IEEE, 2017) Mazenc, F.; Ahmed, Saeed; Özbay, Hitay
We present a new trajectory based approach for state feedback stabilization of switched linear continuous-time systems with a time-varying input delay. In contrast with finding classical common Lyapunov function or multiple Lyapunov functions for establishing the stability of the closed-loop switched system, the new trajectory based approach relies on verifying certain inequalities along the solution of a supplementary system. This study does not make any assumption regarding the stabilizability of all of the constituent subsystems of the switched system. Moreover, no assumption is needed about the differentiability of the delay and no constraint is imposed on the upper bound of the delay derivative. Finally, an illustrative example is included to illustrate the applicability of our results.
Open Access
Switched PD-like controllers for first order unstable systems with time delay
(IFAC, 2009) Arslan, Gül Ezgi; Özbay, Hitay
A new method is proposed for the design of PD-like (first order stable) controllers for switched first order unstable systems with time delays. For this purpose, a dwell-time based stability condition of Yan and Özbay (2008) is used for the class of switched time delay systems studied here. The proposed method finds the values of PD-like controller parameters which minimize an upper bound of the dwell time, minimum time needed between the switching instants to preserve stability. The conservatism analysis of this method is done by time domain simulations. The results show that the calculated upper bound for the dwell time is close to the lower bound of the dwell time observed by simulations.