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  3. consider the state equation (t) = - [o kr] ace), z

Consider the state equation (t) = - [o kr] ace), z(t), 2(T) = 2 (1)...

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Consider the state equation (t) = - [o kr] ace), z(t), 2(T) = 2 (1) 1. Assume that k(t) is constant over time, that is k(t) = k for t > 1. For what value of scalar constant k is the system (1) exponentially stable? 2. Is the state equation (1) uniformly stable for all scalar functions k(t)? If so, provide a proof. If not, provide a counterexample. Consider the state equation (t) = - [o kr] ace), z(t), 2(T) = 2 (1) 1. Assume that k(t) is constant over time, that is k(t) = k for t > 1. For what value of scalar constant k is the system (1) exponentially stable? 2. Is the state equation (1) uniformly stable for all scalar functions k(t)? If so, provide a proof. If not, provide a counterexample

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