João Yoshiyuki Ishihara

On the Lyapunov theorem for singular systems

In this paper, we revisit the Lyapunov theory for singular systems. There are basically two well-known generalized Lyapunov equations used to characterize stability for singular systems. We start with the Lyapunov theorem of the work by Lewis. We show that the Lyapunov equation of that theorem can lead to incorrect conclusion about stability. Some cases where that equation can be used are clarified. We also show that an attempt to correct that theorem with a generalized Lyapunov equation similar to the original one leads naturally to the generalized equation of Takaba et al.

Impulse controllability and observability of rectangular descriptor systems

The presence of impulsive responses in descriptor systems and how it relates to impulse controllability and impulse observability is considered. It is shown that the equivalence between impulse controllability (observability) and the existence of an impulse eliminating semistate feedback (output injection) gain, although true for square descriptor systems, does not hold for rectangular descriptor systems in general. Hence, necessary and sufficient conditions for the existence of an impulse eliminating semistate feedback (output injection) gain are presented.

The full information and state feedback H2 optimal controllers for descriptor systems

In this paper, we consider the full information and the state feedback H2 control problems for continuous-time descriptor systems. An explicit characterization of all optimal controllers is given for these cases. As a consequence, we are able to present a parameterization of all optimal static and dynamic controllers for the LQR problem via state feedback. We also show that, for the general state feedback H2 optimization, the usual gain matrix defined as a linear function of a solution of a generalized Riccati equation can be non-optimal.

Technical Communique: Doubly coprime factorizations related to any stabilizing controllers in state space

Given a plant and an arbitrary stabilizing controller, we present state space formulas for doubly coprime factorizations related to the given controller. Then, we determine parametrizations of all stabilizing controllers centered on that controller.

A new Lyapunov equation for discrete-time descriptor systems

For discrete-time descriptor systems, various generalized Lyapunov equations were studied in the literature. However, these well known generalized Lyapunov equations can be used only under some restrictive assumptions on the plant (as system regularity, or positiveness of a Q matrix, for example). To overcome these limitations, we propose in this paper a new generalized Lyapunov equation for discrete-time descriptor systems.

A new approach to robust linear filtering problems

Abstract This paper deals with optimal filtering problem for uncertain discrete-time systems. The parametric uncertainties are assumed to be norm bounded. It is proposed a robust penalty game approach to solve this problem. The optimum robust filter with the respective recursive Riccati equation proposed are written in a unified framework defined in terms of blocks of matrices. This framework does not depend on any auxiliary parameter to be adjusted. Simulation results show the effectiveness of the robust filter proposed.

Optimal recursive linear filtering for general discrete time singular systems

This paper deals with optimal recursive filtering for time-variant singular systems. The novelty of this paper is the functional developed to deduce this filter in which least squares and penalty functions approaches are combined in a unified way. The advantage of this new procedure will be emphasized in the paper. The nominal singular Kalman filter will be deduced in its most general formulation when the state and measurement noises are correlated. It presents simple and useful symmetric structure.

Control of a Underactuated Manipulator Robot via H 2 , H ∞ , H 2 / H ∞ and µ -Synthesis

Abstract In this paper we perform a comparative study of four combined controllers H 2 H ∞ H 2 / H ∞ and µ plus computed torque method, applied to one real underactuated manipulator robot with 3-degrees of freedom.