Kiyotsugu Takaba

A generalized Lyapunov theorem for descriptor system

Abstract We present a new generalized Lyapunov theorem for a continuous-time descriptor system by extending the theorem due to Lewis (1985). The result is applied to the infinite-horizon descriptor LQ regulator problem.

Stability analysis of networked control systems subject to packet-dropouts and finite-level quantization

This paper is concerned with the stability analysis of a networked control system, wherein communication from the controller to the plant input is through a digital channel subject to packet-dropouts and finite-level quantization. No acknowledgments of receipt are available to the controller. To alleviate the effect of packet-dropouts, the controller transmits tentative plant input sequences. Within this setup, we derive a sufficient condition for small l∞ signal l∞ stability of the networked control system. This condition requires the maximum number of consecutive packet-dropouts to be bounded. We also elucidate the trade-off which exists between the disturbance attenuation and the step size of the quantizer and the maximum number of consecutive packet-dropouts.

Robust H 2 control of descriptor system with time-varying uncertainty

For a descriptor system with time-varying structured uncertainty, this paper considers the robust H 2 control problem of finding a controller satisfying the prescribed H 2 performance level against all possible uncertainty under the constraint of robust stability. A sufficient condition for the robust H2 performance is derived in terms of a linear matrix inequality (LMI). Based on this LMI condition, we develop a design method of a descriptor variable feedback controller achieving the robust performance. The present design method can solve the robust H 2 control problem for a wider class of plants than the state-space approach. A numerical example is also included to show the applicability of the present method.

H2 Output Feedback Control for Descriptor Systems

This paper solves the H^2 output feedback control problem for continuous-time descriptor systems. An existence condition of the H^2 optimal controller is derived based on the standard model matching technique, and a characterization of the optimal controller is given in terms of the solutions of two generalized algebraic Riccati equations. It turns out that the optimal controller has an observer-based structure well-known in the state-space case, so that the results in this paper are natural extensions of the state-space results to the descriptor systems. A numerical example is also included to show the applicability of the proposed results.

Robust servomechanism with preview action for polytopic uncertain systems

This paper considers the robust servomechanism design for a polytopic uncertain system subject to a previewable reference signal. Based on the robust mixed LQ/ℋ∞ criterion, we develop a design method of a state feedback controller with integral and preview actions achieving the robust tracking performance in terms of linear matrix inequalities. A numerical example is also included to show the applicability of the present design method. Copyright

Discrete-time H ∞ algebraic Riccati equation and parametrization of all H ∞ filters

This paper is concerned with the algebraic Riccati equations (AREs) related to the H ∞ filtering problem. A necessary and sufficient condition for the H ∞ problem to be solvable is that the H ∞ ARE has a positive semidefinite stabilizing solution with an additional condition that a certain matrix is positive definite. It is shown that such a stabilizing solution is a monotonically non-increasing convex function of the prescribed H ∞ norm bound γ. This property of the H ∞ ARE is very important for the analysis of the performance of the H ∞ filter. In this paper, the size of the set of all H ∞ filters is considered on the basis of the monotonicity of the above Riccati solution. It turns out that, under a certain condition, the degree of freedom of the H ∞ filter reduces a1 the optimal H ∞ norm bound. These results provide a guideline for selecting the value of γ Some numerical examples are included.

H/sub /spl infin// control for descriptor systems-a J-spectral factorization approach

This paper considers H/sub /spl infin// control for the plant represented by the descriptor form. Using a descriptor version of Youla parametrization, the standard H/sub /spl infin// control problem reduces to a model matching problem (MMP). The J-spectral factorization algorithm in descriptor form is then applied for solving the MMP. The present approach can solve a wider class of H/sub /spl infin// control problems than the state-space approach. A numerical example also shows the applicability of the present approach.<<ETX>>

A Generalized Lyapunov Stability Theorem for Discrete-time Systems based on Quadratic Difference Forms

In this paper, we consider the generalized Lyapunov stability analysis for a discrete-time system described by a high order difference-algebraic equation. In the behavioral approach, a Lyapunov function is characterized in terms of a quadratic difference form. As a main result, we derive a generalized Lyapunov stability theorem that the asymptotic stability of a behavior is equivalent to the solvability of the two-variable polynomial Lyapunov equation (TVPLE) whose solution induces the Lyapunov function. Moreover, we derive another asymptotic stability condition by using a polynomial matrix solution of the one-variable dipolynomial Lyapunov equation which is reduced from the TVPLE.

On the generalized algebraic Riccati equation for continuous-time descriptor systems

Abstract In this paper we consider the generalized algebraic Riccati equation (GARE) for a continuous-time descriptor system. Necessary and sufficient conditions for the existence of stabilizing solutions of the GARE are derived based on the Hamiltonian matrix pencil approach. A parametrization of all stabilizing solutions is also provided. The main result has a potential applicability to a wide class of control problems for a descriptor system, including H 2 / H ∞ controls.

Canonical forms for polynomial and quadratic differential operators

We define the canonical representative for the equivalence class consisting of all polynomial- and quadratic differential operators that take the same values on a given subspace of ℭ^∞(ℝⁿ,ℝ^w). We also examine the relation of this definition with that given in a special case in [17].