Local observer design for nonlinear systems

Vaidyanathan, Sundarapandian

doi:10.1016/s0895-7177(01)00145-5

Cited by 51 publications

(47 citation statements)

References 19 publications

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“…Theorem 3.5 (Sundarapandian, 2002). Suppose that x * is a Lyapunov stable equilibrium of system (5), and that there exists a matrix K such that matrix A − KC is stable, where…”

Section: Is Called a Local Asymptotic (Respectively Exponential) Obsmentioning

confidence: 99%

Observation and control in a model of a cell population affected by radiation

et al. 2009

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The effect of radiation on a cell population is described by a two-dimensional nonlinear system of differential equations. If the radiation rate is not too high, the system is known to have an asymptotically stable equilibrium. First, for the monitoring of this effect, the concept of observability is applied. For the case when the total number of cells is observed, without distinction between healthy and affected cells, a so-called observer system is constructed, which, at least near the equilibrium state, makes it possible to recover the dynamics of both the healthy and the affected cells, from the observation of the total number of cells without distinction.Results of simulations with illustrative data are also presented. If we want to control the system into a required new equilibrium state, and maintain this new equilibrium by a constant control, a technique of theory of optimal control can be applied to construct a feedback control system.

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“…Theorem 3.5 (Sundarapandian, 2002). Suppose that x * is a Lyapunov stable equilibrium of system (5), and that there exists a matrix K such that matrix A − KC is stable, where…”

Section: Is Called a Local Asymptotic (Respectively Exponential) Obsmentioning

confidence: 99%

Observation and control in a model of a cell population affected by radiation

et al. 2009

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“…For the observer design we shall apply the following result (Sundarapandian, 2002): Theorem 2.5. Suppose that system (1) is Lyapunov stable at equilibrium x * , and there exists a matrix K (called gain matrix) such that matrix L − KC is stable.…”

Section: Local Observability and Observer Designmentioning

confidence: 99%

“…Since for frequencydependent selection processes the dynamic model has an invariant manifold, in order to guarantee local observability, we need to apply the linearization method developed in Varga (1992) for systems with invariant manifold. To e ectively recover the genetic process from the phenotypic observation, an observer system will be designed, applying the results of Sundarapandian (2002). In the next section we shortly recall the basic concepts and theorems of the above observability and observer design methodology.…”

Section: Introductionmentioning

confidence: 99%

Observer design for phenotypic observation of genetic processes

López¹,

Gámez²,

Varga³

2008

Nonlinear Analysis: Real World Applications

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In the paper a single-locus sexual population is considered, where the phenotypic selection process is described by an evolutionary game. First, in order to recover the genetic process from di erent observations, observability is guaranteed by the linearization method developed in earlier papers of the authors for systems with invariant manifold. Then, based on a known result of nonlinear systems theory, an observer system is constructed that makes it possible to asymptotically recover the solution of the original system from the observation. In the numerical illustrations the selection is described by a rock-scissors-paper type game widely studied in evolutionary game theory. For the corresponding evolutionary dynamics a Hopf bifurcation result is also obtained.

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“…Then A is stable if and only if a 1 , a 2 > 0. Now, the construction of an observer system will be based on Sundarapandian (2002). …”

Section: Construction Of Local Observersmentioning

confidence: 99%

“…Now we shall apply a similar iterative scheme for the construction and analysis of approximate observers for the monitoring of the state process in a two-species competitive system. Considering a two-species competitive Lotka-Volterra model with a partially monotonous observation, first we find sufficient conditions which make it possible to construct an observer for each member of the sequence of simple auxiliary observation systems, applying the result recalled from Sundarapandian (2002). For earlier applications of observers to systems of population biology see López et al (2007a,b,c).…”

Section: Introductionmentioning

confidence: 99%