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- Control of Complex Nonlinear Systems with Delay
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- Control of complex nonlinear systems with delay [electronic resource] in SearchWorks catalog
This book is a valuable guide for researchers and graduate students in the fields of mathematics, control, and engineering.
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Springer Professional. Back to the search result list. This chapter is dedicated to presenting a new method of saturation nonlinear fields which can be used to tackle problems of analysis and synthesis for linear systems subject to actuator saturations. Noting that new systematic techniques which can be formally presented in the chapter, the objective of the chapter is to show not only the recent methods but also their practical applications. We attempt to provide qualitative analysis methods and stability methods for linear systems with saturated inputs in both global and local contexts.
Our hope is also that this part will enable practitioners to have more concise model systems to modern saturation nonlinear techniques and that this will encourage future applications. In this chapter, commutative matrices of multiple-input multiple-output MIMO linear systems are considered. The existence of the feedback matrices of a commutative state matrix set in the MIMO closed loops is reduced to the existence of an invariant subspace of a matrix A.
The existence of feedback matrices in systems in open loop is equivalent to the existence of the solution of matrix equations denoted by Kronecker products. By defining new equilibrium points, the relationship between equilibrium points is discussed for a linear system with a single saturated input. Four criteria for equilibrium points are outlined for such linear systems. Finally, four interesting examples, including their corresponding simulation plots, are shown to illustrate the above results.
Stability and Control of Nonlinear Time-varying Systems
In this chapter, based on a new method through defining new equilibrium points, the relationship criterion among equilibrium points is discussed for linear system with saturated inputs. The asymptotic stability of the origin of the linear system in the presence of a single saturation input is analyzed, and the existence equations of closed trajectory is also considered for the same control systems.
Finally, characteristics of commutative matrices of MIMO linear systems are considered.
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This chapter is dedicated to presenting equilibrium points for second-order differential systems with single saturated input. The focus of this chapter is on the so-called 0—1 algebra-geometry type structure equations and their equilibrium points under many cases. The chapter attempts to provide constructive qualitative methods on equilibrium points for second-order linear systems with saturated inputs.
By defining new equilibrium points, the relationship between equilibrium points is discussed for second-order linear systems with a single saturated input. Moreover, many interesting examples, including their corresponding stability and possible limited cycles, are effectively shown to illustrate the above results. First, absolute stability criteria, which we define as solvable matrix inequalities, are outlined by constructing a Lyapunov—Razumikhn functional.
Second, we analyze these solvable matrix inequalities, and give their sufficient and necessary solvable conditions that are easily computed in practical systems.
Control of Complex Nonlinear Systems with Delay
Third, based on our norm definition, solvable conditions and time-delay bound estimations can be obtained from two cases of solvable norm inequalities. Finally, an interested numerical example is presented to illustrate the above results effectively.
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It is very difficult in directly analyzing the robust stability of uncertain differential inclusions. If all points of the convex polyhedron are found, we can easily analyze the stability of convex points to obtain the stability of the uncertain differential inclusions. The new method of constructing polyhedron Lyapunov functional for given differential inclusions with nonlinear integral delays is presented. Algebraic criteria of asymptotical stable of the zero solution of a class of differential inclusion with nonlinear integral delays is outlined, too.
Moreover, the above conclusions are similarly generalized to show by the Ricatti matrix inequalities. Finally, an interesting example is presented to illustrate the main result effectively. In this chapter, several new integral inequalities are presented, which are effective in dealing with the integrodifferential inequalities whose variable exponents are greater than 1. Compared with existed integral inequalities, those proposed here can be applied to more complicated differential equations.
In this chapter, the notions of uniform Lipschitz stability are generalized and the relations between these notions are analyzed. Several sufficient conditions about uniform Lipschitz asymptotic stability of nonlinear systems is established by the proposed integral inequalities. These sufficient conditions can be similarly generalized to linearly perturbed differential systems that appear in the literature. Finally, an example of uniform Lipschitz asymptotic stability of nonlinear differential systems is shown. The above sufficient conditions may similarly be generalized to the above time-varying delay neutral differential equations.
Finally, a complex numerical example is presented to illustrate the main result effectively. In order to improve the transmission and safety performance of the single-stage chaotic system, such as chaotic masking, chaotic shift keying, and chaotic modulation, we present a new three-stage chaotic communication system. The chaotic systems in both the transmitter and the receiver end are consisted of the unified chaotic system, which has only one parameter need to be set.
By adjusting the parameters in the linear system and the interference system, we can produce tens of different kinds of transmission signals, which make it more difficult for the illegal receiver to decode the encrypt signal. Kerry J.
About this book
Takahiro Sagawa. Jeffrey Michael McMahon. Nicolas Vogel. George Hasegawa. Jamal Jokar Arsanjani. Florian Buchner. Christopher Race.
Control of complex nonlinear systems with delay [electronic resource] in SearchWorks catalog
Amalio Fernandez-Pacheco. Chiara Gualandi.
Weijia Yuan. Pegor Aynajian. Marco Vignati. Xin Zhang.