Search results for "Lyapunov method"
showing 6 items of 6 documents
STABILITY OF A STOCHASTICALLY PERTURBED MODEL OF INTRACELLULAR SINGLE-STRANDED RNA VIRUS REPLICATION
2019
Compared to the replication of double-stranded RNA and DNA viruses, the replication of single-stranded viruses requires the production of a number of intermediate strands that serve as templates for the synthesis of genomic-sense strands. Two theoretical extreme mechanisms for replication for such single-stranded viruses have been proposed; one extreme being represented by the so-called linear stamping machine and the opposite extreme by the exponential growth. Of course, real systems are more complex and examples have been described in which a combination of such extreme mechanisms can also occur: a fraction of the produced progeny resulting from a stamping-machine type of replication that…
Reference tracking control of hypersonic vehicles using switched linear parameter-varying approach
2013
This paper is concerned with the control problem of the air-breathing hypersonic vehicle using switched linear parameter-varying (LPV) systems approach. By linearizing the nonlinear model of the hypersonic vehicle at trim points and dividing the velocity scope into several partitions, a switched LPV model for the underlying systems is derived. With aid of multiple Lyapunov-like functions technique, the controllers ensuring the tracking of given commands of the closed-loop system are designed under the mode-independent and mode-dependent switching logics, respectively. Simulation results for the hypersonic vehicle show the effectiveness of the proposed method and the advantages of the mode-d…
Robust control of continuous-time systems with state-dependent uncertainties and its application to electronic circuits
2014
In this paper, the problems of robust stability and stabilization are investigated for a class of continuous-time uncertain systems. The uncertainties in the model are state-dependent and belong to a polytopic convex set, as can be found in many electronic circuits and some other applications. The global asymptotic stability conditions for such systems are first established by the classic common quadratic Lyapunov function approach. To reduce conservativeness, a particular class of nonquadratic parameter-dependent Lyapunov functions is introduced, by which improved robust stability conditions for the underlying systems are also derived. Based on the stability criteria, a static output feedb…
Novel Stability Criteria for T--S Fuzzy Systems
2014
In this paper, novel stability conditions for Takagi-Sugeno (T-S) fuzzy systems are presented. The so-called nonquadratic membership-dependent Lyapunov function is first proposed, which is formulated in a higher order form of both the system states and the normalized membership functions than existing techniques in the literature. Then, new membership-dependent stability conditions are developed by the new Lyapunov function approach. It is shown that the conservativeness of the obtained criteria can be further reduced as the degree of the Lyapunov function increases. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the obtained theoretical resul…
Stability analysis of type-2 fuzzy logic controllers
2009
The application of the direct Lyapunov method to the stability analysis of systems controlled by type-2 fuzzy logic controllers (FLC) is presented. The method is an extension of a method proposed for type-1 fuzzy systems. It is usually applied to systems described by state equations and controlled by fuzzy controllers using state variables as inputs but has been extended to controllers that have the error and the integral of error of the controlled variable as inputs. The proposed method allows to modify the controller rule base so that the controlled system is stable in the operating range defined by the manipulative variable constraints. The method is applied to the stability analysis of …
Stability of stochastic nonlinear systems with state-dependent switching
2013
In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô’s formula and Dynkin’s formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-…