Solution and asymptotic behavior of coupled Riccati equations in jump linear systems

Abou-Kandil, Hisham; Freiling, Gerhard; Jank, Gerhard

doi:10.1109/9.310038

Cited by 97 publications

(57 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, we may first solve (34) for , ( ) and . Then, the inequalities (35) are coupled QMIs for ( ), and can be solved by the generalized matrix Riccati inequality/equation approach (see [1]). It remains to focus on the algorithm for solving (34).…”

Section: B Filter Designmentioning

confidence: 99%

Exponential Filtering for Uncertain Markovian Jump Time-Delay Systems With Nonlinear Disturbances

Wang¹,

Lam

Liu³

2004

IEEE Trans. Circuits Syst. II

139

View full text Add to dashboard Cite

Abstract-In this paper, we study the robust exponential filter design problem for a class of uncertain time-delay systems with both Markovian jumping parameters and nonlinear disturbances. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainties appearing in the state and output equations are real, time dependent, and norm bounded. The time-delay and the nonlinear disturbances are assumed to be unknown. The purpose of the problem under investigation is to design a linear, delay-free, uncertainty-independent state estimator such that, for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. We address both the filtering analysis and synthesis issues, and show that the problem of exponential filtering for the class of uncertain time-delay jump systems with nonlinear disturbances can be solved in terms of the solutions to a set of linear (quadratic) matrix inequalities. A numerical example is exploited to demonstrate the usefulness of the developed theory.

show abstract

Section: B Filter Designmentioning

confidence: 99%

Exponential Filtering for Uncertain Markovian Jump Time-Delay Systems With Nonlinear Disturbances

Wang¹,

Lam

Liu³

2004

IEEE Trans. Circuits Syst. II

139

View full text Add to dashboard Cite

show abstract

“…Generalized Riccati equations of this form appear when studying optimal control of linear systems with Markovian jumps (see [1], [21], [28], and [8] for a detailed description and further references). Such equations also occur in robust control problems (see [19]) and for the discrete time case (see [18]).…”

Section: = Ric (W H) -Ix(w)mentioning

confidence: 99%

Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations

Freiling

Jank

1996

Journal of Dynamical and Control Systems

Self Cite

View full text Add to dashboard Cite

ABSTRACT. We present comparison and global existence theorems for solutions of generalized matrix Riccati differential and difference equations. Moreover we obtain existence and comparison results for the maximal solutions of the corresponding generalized algebraic Riccati equations. For the symplectic matrix Riccati differential equation we derive sufficient conditions ensuring the global existence of the solutions of the corresponding initial value problems.

show abstract

“…Here we investigate, in detail, a method based on the ergodic property of recurrence; other methods include the jump linear approximation [1], [9], [10], and the method based on iterating the Riccati recursion (11).…”

Section: Exploiting Ergodicity To Solve the Functional Algebraic Rmentioning

confidence: 99%

“…Since varies according to the dynamical equation (1), such an interconnection as (1) and (3) is called an LDV system. LDV and linear parametrically varying (LPV) system can be unified under the so-called linear set-valued dynamically varying (LSVDV) systems characterized by a set-valued map [17].…”

Section: Linear Dynamically Varying Tracking Error Dynamicsmentioning

confidence: 99%

Linear dynamically varying LQ control of nonlinear systems over compact sets

Bohacek

Jonckheere²

2001

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

Abstract-Linear-quadratic controllers for tracking natural and composite trajectories of nonlinear dynamical systems evoluting over compact sets are developed. Typically, such systems exhibit "complicated dynamics," i.e., have nontrivial recurrence. The controllers, which use small perturbations of the nominal dynamics as input actuators, are based on modeling the tracking error as a linear dynamically varying (LDV) system. Necessary and sufficient conditions for the existence of such a controller are linked to the existence of a bounded solution to a functional algebraic Riccati equation (FARE). It is shown that, despite the lack of continuity of the asymptotic trajectory relative to initial conditions, the cost to stabilize about the trajectory, as given by the solution to the FARE, is continuous. An ergodic theory method for solving the FARE is presented. Furthermore, it is shown that wrapping the LDV controller around the nonlinear system secures a stable tracking dynamics. Finally, an example of controlling the Hénon map to follow an aperiodic orbit is presented.

show abstract

Solution and asymptotic behavior of coupled Riccati equations in jump linear systems

Cited by 97 publications

References 14 publications

Exponential Filtering for Uncertain Markovian Jump Time-Delay Systems With Nonlinear Disturbances

Exponential Filtering for Uncertain Markovian Jump Time-Delay Systems With Nonlinear Disturbances

Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations

Linear dynamically varying LQ control of nonlinear systems over compact sets

Contact Info

Product

Resources

About