Browsing by Author "Zakwan, Muhammad"

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Open Access
Conewise linear systems: a characterization of transitive cones in 3D-space
(The European Control Association (EUCA), 2019-06) Özgüler, A. Bülent; Zakwan, Muhammad
A spatial (3D) piecewise linear system with multiple modes having conewise state spaces is considered. A single mode in this system is called transitive from one (respectively, two) of its borders if every trajectory that starts in its interior or at a border travels in its interior, hits that border (respectively, one of the two borders), and goes out of the cone. This paper characterizes transitive cones in case the dynamics in the cone is dictated by real and distinct eigenvalues. An example of a 3D piecewise linear system composed of transitive cones illustrates how a nonlinear oscillator can be synthesized.
Open Access
Distributed output feedback control of decomposable LPV systems with delay and switching topology: application to consensus problem in multi-agent systems
(Taylor & Francis, 2020-01-08) Zakwan, Muhammad; Ahmed, Saeed
This paper presents distributed output feedback control of a class of distributed linear parameter varying systems with switching topology and parameter varying time delay. To formulate the synthesis conditions for the distributed controller in terms of LMIs, the delay dependent bounded-real lemma based on parameter-dependent Lyapunov–Krasovskii functionals is used. The efficacy of the result is illustrated by applying it to two real-world examples pertaining to the consensus problem of multi-agent systems.
Open Access
Distributed output feedback control of decomposable lpv systems with delay: application to multi-agent nonholonomic systems
(IEEE, 2019) Zakwan, Muhammad; Ahmed, Saeed
This paper presents distributed output feedback control of a class of distributed linear parameter varying systems with a parameter-dependent time-varying delay. A delaydependent bounded-real lemma approach, based on parameterdependent Lyapunov-Krasovskii functionals, is used to formulate the synthesis condition in terms of linear matrix inequalities. We demonstrate the efficacy of our result by applying it to formation control of multi-agent nonholonomic mobile robots.
Open Access
Dynamic L2 output feedback stabilization of LPV systems with piecewise constant parameters subject to spontaneous poissonian jumps
(IEEE, 2020) Zakwan, Muhammad
This letter addresses the L 2 output feedback stabilization of linear parameter varying systems, where the parameters are assumed to be stochastic piecewise constants under spontaneous Poissonian jumps. We provide sufficient conditions in terms of linear matrix inequalities (LMIs) for the existence of a full-order output feedback controller. Such LMIs, however, can be computationally intractable due to the presence of integral terms. Nevertheless, we show that these LMIs can be equivalently represented by an integral-free LMI, which is computationally tractable. Finally, we provide analytical formulas to construct the controller and illustrate the applicability of the results through examples.
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.