Nonlinear Systems Analysis

Vidyasagar, M.

doi:10.1137/1.9780898719185

Cited by 761 publications

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“…The region-of-attraction R 0 of the origin for the system (1) is R 0 := {ξ ∈ R n : lim t→∞ φ(ξ, t) = 0} . A modification of a similar result in (Vidyasagar, 1993) provides a characterization of invariant subsets of the ROA. For η > 0 and a function V :…”

Section: Introductionmentioning

confidence: 91%

Local stability analysis using simulations and sum-of-squares programming

2008

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Section: Introductionmentioning

confidence: 91%

Local stability analysis using simulations and sum-of-squares programming

2008

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“…exists and x(I(x(0))) ∈ K. However, we could use again Theorem 2.2 with I(x(0)) as the initial time and x(I(x(0))) as the initial state to show the existence of solution of (1) on 45th IEEE CDC, San Diego, USA, Dec. [13][14][15]2006 WeB10.6…”

Section: Definition 21mentioning

confidence: 99%

“…It is easy to see from (8) )). Therefore, the system P as in Theorem 3.2 is L p -stable and it has a finite L p -gain (see Vidyasagar 45th IEEE CDC, San Diego, USA, Dec. [13][14][15]2006 WeB10.6 [15] or van der Schaft [9] for details). It will be shown in Example 5.2 and Corollary 5.3 below that the Assumptions (A1) and (A2) are sufficient conditions for P being L p -stable.…”

Section: Remark 34mentioning

confidence: 99%

Remarks on the state convergence of nonlinear systems given any Lp input

Jayawardhana

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-In this paper, we study the state convergence of L pstable systems and input-to-state stable (ISS) systems given any L p input signal where p ∈ [1, ∞). Under some conditions on the system equations, it is shown that if the system is dissipative with a proper storage function H and supply rate s(y, u) = u p − k y p , k > 0 and it is zero-state detectable then the state x of the system converges to zero for any L p input. This implies also that the system is also L p -stable.Using the same technique, if the system is ISS, under some conditions on the system equations and on the smooth ISS Lyapunov function, then the state x of the system converges to zero for any L p input.

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“…Dynamical system theory aims to characterize systems via time-evolution models [1,2]. Such characterization can be employed for performing two fundamental and dual tasks in dynamical system theory: on the one hand, the estimation of system's internal state from the measurement of accessible system outputs, defining the so called observation problem; on the other hand, the modification of system's internal state via the injection of appropriate system inputs, defining the so called control problem [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

Controlling Systems with a Single Actuator

Portal

Zufiria

2015

Liss 2014

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Abstract. In this paper the problem of designing a single actuator control for a class of systems is addressed. The existence of such control is studied and several ways for designing such control are provided. The results depend either on the rational canonical form or on the Jordan structure associated with the matrix which characterizes the system dynamics. The constructed control laws can be employed in the design of minimum cost controllers for a large variety of systems.Keywords: Controllability • rational Frobenius form • Jordan form IntroductionDynamical system theory aims to characterize systems via time-evolution models [1,2]. Such characterization can be employed for performing two fundamental and dual tasks in dynamical system theory: on the one hand, the estimation of system's internal state from the measurement of accessible system outputs, defining the so called observation problem; on the other hand, the modification of system's internal state via the injection of appropriate system inputs, defining the so called control problem [3,4,5]. These problems have been thoroughly studied in the literature, specially for linear systems [6,7,3]. A fundamental issue when dealing with the control and observation of dynamical systems is that of the controllability and observability of the system, i.e. under which conditions a system can be controlled or observed. Such conditions are well established for the case of linear time invariant (LTI) dynamical systems of the form ^ = Ax(t) +Bu(t), y(t) = Cx(t), where Many standard control problems have to deal with matrices A and B which are prestablished by the system dynamics and/or actuator restrictions. In this context, the controllability condition serves as a test on the existence of control laws with some specific properties. On the other hand, some applications or theoretical problems consider the possibility of arbitrarily selecting the number and location of the actuators. Hence, matrix B may become a design element, and the controllability condition may serve as a design criterion. In

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Nonlinear Systems Analysis

Cited by 761 publications

References 0 publications

Local stability analysis using simulations and sum-of-squares programming

Local stability analysis using simulations and sum-of-squares programming

Remarks on the state convergence of nonlinear systems given any Lp input

Controlling Systems with a Single Actuator

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