Design of bounded feedback controls for linear dynamical systems by using common Lyapunov functions

For a linear dynamical system,we address the problem of devising a bounded feedback control,which brings the system to the origin in finite time.The construction is based on the notion of a common Lyapunov function.It is shown that the constructed control remains effective in the presence of small perturbations.

Solid State Bioconversion for Producing Common Bean(Phaseolus vulgaris L.)Functional Flour with High Antioxidant Activity and Antihypertensive Potential

The main objective of this investigation was to study the time effect during solid state bioconversion (SSB) on total phenolics content (TPC) and antioxidant activity (AoxA) of common beans to improve antihypertensive functionality. Cooked cotyledons of dehulled common beans were inoculated with a suspension of R. oligosporus NRRL 2710 (1 × 106 spores/mL), and incubated at 35℃ for times of 24, 36, 48, 60, 72, 84, 96 and 108 h (after 108 h the cotyledons showed off odor). Flours from bioprocessed dehulled common bean from each incubation time were blended with their corresponding milled seed coats. The best time for producing bioprocessed common bean (added with seed coats) functional flour with the highest AoxA (ORAC value = 17,468 μmol Trolox equivalents (TE)/100 gsample, dw;ABTS value = 13,505 μmol TE/100 gsample, dw) was 108 h. The SSB process substantially increased TPC and total hydrophilic AoxA and antihypertensive potential of common beans in 2.24, 2.45 - 2.73 and 6769 times, respectively. Proteins hydrolyzates from unprocessed whole and bioprocessed (108 h) common beans had IC50 [concentration needed to inhibit 50% the activity of angiotensin converting enzyme (ACE)] of 79.2 and 0.0117 μg/mL, respectively. The SSB is an efective strategy to improve the TPC of common beans for enhanced functionality with improved antioxidant activity and antihypertensive potential.

Effect of Mercuric Chloride and Cadmium Chloride on Gonadal Function and Its Regulation in SexuallyMature Common Carp Cyprinus carpio

Gonadal function in fish, CJprinus carpio was significantly affected by sublethal doses of mercuric chloride (HgCl2 ) and cadmium chloride (CdCl2 ) in chronic (45 days ) exposure.Parameters investigated were nonesterified (NE) and esterified (E) cholestcrol of ovary,liver and serum and ovarian 3β-Hydroxysteroid and 17β-Hydroxysteroid dehyrogenaseenzyme activity and serum and pituitary gonadotropin (GtH) levels. Both the pollutantswere able to reduce the hypothalamic extract (HE) or gonadotropin releasing hormone(GnRH) induced pituitary GtH release in vitro. Short term (96h) exposure of the fish tothe pollutants had no significant effect on the gonadal function. ln addition to thedeleterious effect of pollutants on the gonadal steroidogenesis and pituitary gonadotropin release, using [4-14C] cholesterol as a tracer it was found that for 45 days expeure, HgCl2'had an adverse effect on the transport of cholesterol from circulation to ovary.

Control of switched systems with actuator saturation

This paper is concerned with controller synthesis for linear switched systems with actuator saturation. Based on common Lyapunov function technique and multiple-Lyapunov function technique, two methods for designing state feedback controller are proposed respectively in terms of linear matrix inequalities for the switched systems with saturation. An approach on enlarging the attractive domain is then investigated, The application of the presented approach is illustrated finally by a numerical example.

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of （generalized） switched Byrnes-Isidori canonical form, which has all switched models in （generalized） Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to （generalized） switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.

Stability and Stabilization of Block-cascading Switched Linear Systems

The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is （QLFs） is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.

Stability of General Linear Dynamic Multi-Agent Systems under Switching Topologies with Positive Real Eigenvlues

The time-varying network topology can significantly affect the stability of multi-agent systems.This paper examines the stability of leader-follower multi-agent systems with general linear dynamics and switching network topologies,which have applications in the platooning of connected vehicles.The switching interaction topology is modeled as a class of directed graphs in order to describe the information exchange between multi-agent systems,where the eigenvalues of every associated matrix are required to be positive real.The Hurwitz criterion and the Riccati inequality are used to design a distributed control law and estimate the convergence speed of the closed-loop system.A sufficient condition is provided for the stability of multi-agent systems under switching topologies.A common Lyapunov function is formulated to prove closed-loop stability for the directed network with switching topologies.The result is applied to a typical cyber-physical system—that is,a connected vehicle platoon—which illustrates the effectiveness of the proposed method.

H-infinity control for cascade minimum-phase switched nonlinear systems

This paper is concerned with the H-infinity control problem for a class of cascade switched nonlinear systems. Each switched system in this class is composed of a zero-mput asymptotically stable nonlinear part, which is also a switched system, and a linearizable part which is controllable. Conditions under which the H-infinity control problem is solvable under arbitrary switching law and under some designed switching law are derived respectively. The nonlinear state feedback and switching law are designed. We exploit the structural characteristics of the switched nonlinear systems to construct common Lyapunov functions for arbitrary switching and to find a single Lyapunov function for designed switching law. The proposed methods do not rely on the solutions of Hamilton-Jacobi inequalities.

Adaptive fuzzy tracking control for a class of switched MIMO nonlinear systems

An adaptive fuzzy tracking control scheme is presented for a class of switched multi-input-multi-output (MIMO) nonlinear systems with disturbances under arbitrary switching. Adaptive fuzzy systems are employed to approximate the unknown functions on line,and a systematic framework for adaptive fuzzy tracking controller design is given,where the dynamic surface control (DSC) approach is used to solve the problem of "explosion of complexity"in the backstepping design procedure. According to the common Lyapunov function theory,it is proved that the proposed controller can guarantee the boundedness of all signals in the closed loop system. Finally,the simulation results demonstrate the validity of the control approach.

On Two Problems for Matrix Polytopes

We consider two problems from stability theory of matrix polytopes: the existence of common quadratic Lyapunov functions and the existence of a stable member. We show the applicability of the gradient algorithm and give a new sufficient condition for the second problem. A number of examples are considered.

On Asymptotic Stability of Linear Control Systems

Asymptotic stability of linear systems is closely related to Hurwitz stability of the system matrices. For uncertain linear systems we consider stability problem through common quadratic Lyapunov functions (CQLF) and problem of stabilization by linear feedback.

Safety stabilization of switched systems with unstable subsystems

This paper is concerned with the problem of safety stabilization for switched systems where the solvability of the problem under study for individual subsystems is not assumed.A new state-dependent switching strategy with guaranteed dwell-time for switched systems is constructed,and a sufficient condition for absence of Zeno behavior is derived.Also,a novel switched control design method is proposed to simultaneously guarantee the safety of the switched closed-loop system and stabilize the system based on the union of a common barrier function and a single Lyapunov function,which effectively handles the conflict between safety and stability objectives.Finally,two examples are presented to demonstrate the effectiveness of the proposed design approach.

Stability of switched nonlinear systems via extensions of LaSalle's invariance principle

This paper studies the extension of LaSalle＇s invariance principle for switched nonlinear systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows the switching modes to be only stable. Under certain ergodicity assumptions of the switching signals, two extensions of LaSalle＇s invariance principle for global asymptotic stability of switched nonlinear systems are obtained using the method of common joint Lyapunov function.

Regional Stability of Positive Switched Linear Systems with Multi-equilibrium Points

This paper studies the regional stability for positive switched linear systems with multi-equilibrium points （PSLS-MEP）. First, a sufficient condition is presented for the regional stability of PSLS-MEP via a common linear Lyapunov function. Second, by establishing multiple Lyapunov functions, a dwell time based condition is proposed for the regional stability analysis. Third, a suprasphere which contains all equilibrium points is constructed as a stability region of the considered PSLS-MEP, which is less conservative than existing results. Finally, the study of an illustrative example shows that the obtained results are effective in the regional stability analysis of PSLS-MEP.

A computing capability test for a switched system control design using the Haris-Rogers method

The problem of finding stabilizing controllers for switched systems is an area of much research interest as conventional concepts from continuous time and discrete event dynamics do not hold true for these systems.Many solutions have been proposed,most of which are based on finding the existence of a common Lyapunov function(CLF) or a multiple Lyapunov function(MLF) where the key is to formulate the problem into a set of linear matrix inequalities(LMIs).An alternative method for finding the existence of a CLF by solving two sets of linear inequalities(LIs) has previously been presented.This method is seen to be less computationally taxing compared to methods based on solving LMIs.To substantiate this,the computational ability of three numerical computational solvers,LMI solver,cvx,and Yalmip,as well as the symbolic computational program Maple were tested.A specific switched system comprising four second-order subsystems was used as a test case.From the obtained solutions,the validity of the controllers and the corresponding CLF was verified.It was found that all tested solvers were able to correctly solve the LIs.The issue of rounding-off error in numerical computation based software is discussed in detail.The test revealed that the guarantee of stability became uncertain when the rounding off was at a different decimal precision.The use of different external solvers led to the same conclusion in terms of the stability of switched systems.As a result,a shift from using a conventional numerical computation based program to using computer algebra is suggested.

Quadratic stabilization of switched nonlinear systems

In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated.When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law.The results of this paper are also applied to switched linear systems.