State-space analysis of finite dimensional continuous and discrete time linear systems. Linear vector spaces, linear operators, normed linear spaces, and inner product spaces. Fundamentals of matrix algebra; generalized inverses, solution of Ax=y and AXB=Y, least square and recursive least square estimation, induced norm and matrix measures, functions of a square matrix, Cayley-Hamilton and Sylvester's theorems, Singular Value Decomposition (SVD) with applications. Analytical representation of linear systems, state-space formulation, solution of the state equation and determination of the system's response. Controllability, observability, duality, canonical forms, and minimal realization concepts. Stability analysis and the Lyapunov's method. Prerequisite: Graduate standing.
State-space analysis of finite dimensional continuous and discrete time linear systems. Linear vector spaces, linear operators, normed linear spaces, and inner product spaces. Fundamentals of matrix algebra; generalized inverses, solution of Ax=y and AXB=Y, least square and recursive least square estimation, induced norm and matrix measures, functions of a square matrix, Cayley-Hamilton and Sylvester's theorems, Singular Value Decomposition (SVD) with applications. Analytical representation of linear systems, state-space formulation, solution of the state equation and determination of the system's response. Controllability, observability, duality, canonical forms, and minimal realization concepts. Stability analysis and the Lyapunov's method. Prerequisite: Graduate standing.
